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Finite determinacy and stability of flatness of analytic mappings Adamus, Janusz; Seyedinejad, Hadi Published: 20160429
It is proved that flatness of an analytic mapping germ from a
complete intersection is determined by its sufficiently high
jet. As a consequence, one obtains finite determinacy of complete
intersections. It is also shown that flatness and openness are
stable under deformations.


Dynamics and regularization of the Kepler problem on surfaces of constant curvature Andrade, Jaime; Dávila, Nestor; PérezChavela, Ernesto; Vidal, Claudio Published: 20160617
We classify and analyze the orbits of the Kepler problem on surfaces
of constant curvature (both positive and negative, $\mathbb S^2$ and
$\mathbb H^2$, respectively) as function of the angular momentum and
the energy. Hill's region are characterized and the problem of
timecollision is studied. We also regularize the problem in
Cartesian and intrinsic coordinates, depending on the constant
angular momentum and we describe the orbits of the regularized
vector field. The phase portrait both for $\mathbb S^2$ and $\mathbb H^2$
are pointed out.


Monodromy action on unknotting tunnels in fiber surfaces Banks, Jessica; Rathbun, Matt Published: 20160623
In \cite{RatTOFL}, the second author showed that a tunnel of a tunnel
number one, fibered link in $S^3$ can be isotoped to lie as a properly
embedded arc in the fiber surface of the link. In this paper, we
observe that this is true for fibered links in any 3manifold, we
analyze how the arc behaves under the monodromy action, and we show
that the tunnel arc is nearly clean, with the possible exception of
twisting around the boundary of the fiber.


Simultaneous additive equations: Repeated and differing degrees Brandes, Julia; Parsell, Scott T. Published: 20160621
We obtain bounds for the number of variables required to establish
Hasse principles, both for existence of solutions and for asymptotic
formulæ, for systems of additive equations containing forms
of differing degree but also multiple forms of like degree.
Apart from the very general estimates of Schmidt and BrowningHeathBrown,
which give weak results when specialized to the diagonal situation,
this is the first result on such "hybrid" systems. We also obtain
specialised results for systems of quadratic and cubic forms,
where we are able to take advantage of some of the stronger methods
available in that setting. In particular, we achieve essentially
square root cancellation for systems consisting of one cubic
and $r$ quadratic equations.


Eigenvarieties for cuspforms over PEL type Shimura varieties with dense ordinary locus Brasca, Riccardo Published: 20160510
Let $p \gt 2$ be a prime and let $X$ be a compactified PEL Shimura
variety of type (A) or (C) such that $p$ is an unramified prime
for the PEL datum and such that the ordinary locus is dense in
the reduction of $X$. Using the geometric approach of Andreatta,
Iovita, Pilloni, and Stevens we define the notion of families
of overconvergent locally analytic $p$adic modular forms of
Iwahoric level for $X$. We show that the system of eigenvalues
of any finite slope cuspidal eigenform of Iwahoric level can
be deformed to a family of systems of eigenvalues living over
an open subset of the weight space. To prove these results, we
actually construct eigenvarieties of the expected dimension that
parameterize finite slope systems of eigenvalues appearing in
the space of families of cuspidal forms.


Stability for the BrunnMinkowski and Riesz rearrangement inequalities, with applications to Gaussian concentration and finite range nonlocal isoperimetry Carlen, Eric; Maggi, Francesco Author's Draft
We provide a simple, general argument to obtain improvements
of concentrationtype inequalities starting from improvements
of their corresponding isoperimetrictype inequalities. We apply
this argument to obtain robust improvements of the BrunnMinkowski
inequality (for Minkowski sums between generic sets and convex
sets) and of the Gaussian concentration inequality. The former
inequality is then used to obtain a robust improvement of the
Riesz rearrangement inequality under certain natural conditions.
These conditions are compatible with the applications to a finiterange
nonlocal isoperimetric problem arising in statistical mechanics.


Sharp norm estimates for the Bergman operator from weighted mixednorm spaces to weighted Hardy spaces Cascante, Carme; Fàbrega, Joan; Ortega, Joaquín M. Published: 20160418
In this paper we give sharp norm estimates for the Bergman operator
acting from weighted
mixednorm spaces to weighted Hardy spaces in the ball,
endowed with natural norms.


Convolution powers of Salem measures with applications Chen, Xianghong; Seeger, Andreas Author's Draft
We study the regularity of convolution powers for measures supported
on
Salem sets, and prove related results on Fourier restriction
and Fourier multipliers. In particular we show
that for $\alpha$ of the form
${d}/{n}$, $n=2,3,\dots$ there exist $\alpha$Salem measures
for which the $L^2$ Fourier restriction theorem holds in the
range $p\le \frac{2d}{2d\alpha}$.
The results rely on ideas of Körner.
We extend some of his constructions to obtain upper regular $\alpha$Salem
measures, with sharp regularity results for $n$fold convolutions
for all $n\in \mathbb{N}$.


Transport inequalities for logconcave measures, quantitative forms and applications CorderoErausquin, Dario Author's Draft
We review some simple techniques based on monotone mass transport
that allow to obtain transporttype inequalities for any logconcave
probability measure. We discuss quantitative forms of these inequalities,
with application to the variance BrascampLieb inequality.


Tilings of normed spaces De Bernardi, Carlo Alberto; Veselý, Libor Published: 20160308
By a tiling of a topological linear space $X$ we mean a
covering of $X$ by at least two closed convex sets,
called tiles, whose nonempty interiors are
pairwise disjoint.
Study of tilings of infinitedimensional spaces initiated in
the
1980's with pioneer papers by V. Klee.
We prove some general properties of tilings of locally convex
spaces,
and then apply these results to study existence of tilings of
normed and Banach spaces by tiles possessing
certain smoothness or rotundity properties. For a Banach space
$X$,
our main results are the following.


A class of degenerate elliptic equations with nonlinear boundary conditions Du, Zhuoran; Fang, Yanqin; Gui, Changfeng Published: 20160627
We consider positive solutions of the problem
\begin{equation}
(*)\qquad
\left\{
\begin{array}{l}\mbox{div}(x_{n}^{a}\nabla u)=bx_{n}^{a}u^{p}\;\;\;\;\;\mbox{in}\;\;\mathbb{R}_{+}^{n},
\\
\frac{\partial u}{\partial \nu^a}=u^{q} \;\;\;\;\;\;\;\;
\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mbox{on}\;\;\partial \mathbb{R}_{+}^{n},
\\
\end{array}
\right.
\end{equation}
where $a\in (1,0)\cup(0,1)$, $b\geq 0$, $p, q\gt 1$ and
$\frac{\partial u}{\partial \nu^a}:=\lim_{x_{n}\rightarrow
0^+}x_{n}^{a}\frac{\partial u}{\partial x_{n}}$. In special case
$b=0$, it is associated to fractional Laplacian equation $(\Delta)^{s}u=u^{q}
$ in entire space $\mathbb{R}^{n1}$.
We obtain the existence of positive axially symmetric solutions
to ($*$) for the case $a\in
(1,0)$ in
$n\geq3$ for supercritical exponents $p\geq\frac{n+a+2}{n+a2},
\;\;q\geq\frac{na}{n+a2}$.
The nonexistence is obtained for the case $a\in (1,0)$, $b\geq
0$ and any $p,~q\gt 1$ in $n=2$ as well.


2row Springer fibres and Khovanov diagram algebras for type D Ehrig, Michael; Stroppel, Catharina Published: 20160719
We study in detail two row Springer fibres of even orthogonal
type from an algebraic as well as topological point of view.
We show that the irreducible components and their pairwise intersections
are iterated $\mathbb{P}^1$bundles. Using results of Kumar and Procesi
we compute the cohomology ring with its action of the Weyl group.
The main tool is a type $\operatorname D$ diagram calculus labelling the
irreducible components in a convenient way which relates to a
diagrammatical algebra describing the category of perverse sheaves
on isotropic Grassmannians based on work of Braden. The diagram
calculus generalizes Khovanov's arc algebra to the type
$\operatorname
D$ setting and should be seen as setting the framework for generalizing
wellknown connections of these algebras in type $\operatorname A$ to other
types.


Splitting, Bounding, and Almost Disjointness can be quite Different Fischer, Vera; Mejia, Diego Alejandro Published: 20160719
We prove the consistency of
$$
\operatorname{add}(\mathcal{N})\lt
\operatorname{cov}(\mathcal{N})
\lt \mathfrak{p}=\mathfrak{s}
=\mathfrak{g}\lt \operatorname{add}(\mathcal{M})
= \operatorname{cof}(\mathcal{M}) \lt \mathfrak{a}
=\mathfrak{r}=\operatorname{non}(\mathcal{N})=\mathfrak{c}
$$
with $\mathrm{ZFC}$, where each of these cardinal
invariants assume arbitrary
uncountable regular values.


Dirichlet's theorem in function fields Ganguly, Arijit; Ghosh, Anish Published: 20160729
We study metric Diophantine approximation for function fields
specifically the problem of improving Dirichlet's theorem in
Diophantine
approximation.


On K3 surface quotients of K3 or Abelian surfaces Garbagnati, Alice Published: 20160318
The aim of this paper is to prove that a K3 surface is the minimal
model of the quotient of an Abelian surface by a group $G$ (respectively
of a K3 surface by an Abelian group $G$) if and only if a certain
lattice is primitively embedded in its NéronSeveri group.
This allows one to describe the coarse moduli space of the K3
surfaces which are (rationally) $G$covered by Abelian or K3
surfaces (in the latter case $G$ is an Abelian group).
If either $G$ has order 2 or $G$ is cyclic and acts on an Abelian
surface, this result was already known, so we extend it to the
other cases.


Dual immaculate creation operators and a dendriform algebra structure on the quasisymmetric functions Grinberg, Darij Published: 20160712
The dual immaculate functions are a basis of the ring $\operatorname*{QSym}$
of quasisymmetric functions, and form one of the most natural
analogues of the
Schur functions. The dual immaculate function corresponding to
a composition
is a weighted generating function for immaculate tableaux in
the same way as a
Schur function is for semistandard Young tableaux; an "
immaculate tableau" is defined similarly to be
a semistandard
Young tableau, but the shape is a composition rather than a partition,
and
only the first column is required to strictly increase (whereas
the other
columns can be arbitrary; but each row has to weakly increase).
Dual
immaculate functions have been introduced by Berg, Bergeron,
Saliola, Serrano
and Zabrocki in arXiv:1208.5191, and have since been found to
possess numerous
nontrivial properties.


$L^q$ norms of Fekete and related polynomials Günther, Christian; Schmidt, KaiUwe Published: 20160628
A Littlewood polynomial is a polynomial in $\mathbb{C}[z]$ having all
of its coefficients in $\{1,1\}$. There are various old unsolved
problems, mostly due to Littlewood and Erdős, that ask for
Littlewood polynomials that provide a good approximation to a
function that is constant on the complex unit circle, and in
particular have small $L^q$ norm on the complex unit circle.
We consider the Fekete polynomials
\[
f_p(z)=\sum_{j=1}^{p1}(j\,\,p)\,z^j,
\]
where $p$ is an odd prime and $(\,\cdot\,\,p)$ is the Legendre
symbol (so that $z^{1}f_p(z)$ is a Littlewood polynomial). We
give explicit and recursive formulas for the limit of the ratio
of $L^q$ and $L^2$ norm of $f_p$ when $q$ is an even positive
integer and $p\to\infty$. To our knowledge, these are the first
results that give these limiting values for specific sequences
of nontrivial Littlewood polynomials and infinitely many $q$.
Similar results are given for polynomials obtained by cyclically
permuting the coefficients of Fekete polynomials and for Littlewood
polynomials whose coefficients are obtained from additive characters
of finite fields. These results vastly generalise earlier results
on the $L^4$ norm of these polynomials.


Free product C*algebras associated to graphs, free differentials, and laws of loops Hartglass, Michael Author's Draft
We study a canonical C$^*$algebra, $\mathcal{S}(\Gamma, \mu)$, that
arises from a weighted graph $(\Gamma, \mu)$, specific cases
of which were previously studied in the context of planar algebras.
We discuss necessary and sufficient conditions of the weighting
which ensure simplicity and uniqueness of trace of $\mathcal{S}(\Gamma,
\mu)$, and study the structure of its positive cone. We then
study the $*$algebra, $\mathcal{A}$, generated by the generators of
$\mathcal{S}(\Gamma, \mu)$, and use a free differential calculus and
techniques of Charlesworth and Shlyakhtenko, as well as Mai,
Speicher, and Weber to show that certain ``loop" elements have
no atoms in their spectral measure. After modifying techniques
of Shlyakhtenko and Skoufranis to show that self adjoint elements
$x \in M_{n}(\mathcal{A})$ have algebraic Cauchy transform, we explore
some applications to eigenvalues of polynomials in Wishart matrices
and to diagrammatic elements in von Neumann algebras initially
considered by Guionnet, Jones, and Shlyakhtenko.


On the isomorphism problem for multiplier algebras of NevanlinnaPick spaces Hartz, Michael Published: 20160510
We continue the investigation of the isomorphism problem for
multiplier algebras of reproducing kernel
Hilbert spaces with the complete NevanlinnaPick property.
In contrast to previous work in this area,
we do not study these spaces by identifying them with restrictions
of a universal space, namely the DruryArveson space.
Instead, we work directly with the Hilbert spaces and their
reproducing kernels. In particular,
we show that two multiplier algebras of NevanlinnaPick spaces
on the same set are equal if and only if the Hilbert
spaces are equal. Most of the article is devoted to the study
of a special class of
complete NevanlinnaPick spaces on homogeneous varieties. We
provide a complete
answer to the question of when two multiplier algebras of spaces
of this type
are algebraically or isometrically isomorphic. This generalizes
results of Davidson, Ramsey, Shalit,
and the author.


On the Neumann problem for MongeAmpère type equations Jiang, Feida; Trudinger, Neil S; Xiang, Ni Published: 20160621
In this paper, we study the global regularity for
regular
MongeAmpère type equations associated with semilinear Neumann
boundary conditions.
By establishing a priori estimates for second order derivatives,
the
classical solvability of the Neumann boundary value problem is
proved under natural conditions.
The techniques build upon the delicate and intricate treatment
of the standard MongeAmpère case
by Lions, Trudinger and Urbas in 1986 and the recent barrier
constructions and second derivative bounds
by Jiang, Trudinger and Yang for the Dirichlet problem. We also
consider more general oblique boundary
value problems in the strictly regular case.


Strict comparison of positive elements in multiplier algebras Kaftal, Victor; Ng, Ping Wong; Zhang, Shuang Published: 20160628
Main result: If a C*algebra $\mathcal{A}$ is simple, $\sigma$unital,
has finitely many extremal traces, and has strict comparison
of positive elements by traces, then its multiplier algebra
$\operatorname{\mathcal{M}}(\mathcal{A})$
also has strict comparison of positive elements by traces. The
same results holds if ``finitely many extremal traces" is replaced
by ``quasicontinuous scale".
A key ingredient in the proof is that every positive element
in the multiplier algebra of an arbitrary $\sigma$unital C*algebra
can be approximated by a bidiagonal series.
An application of strict comparison: If $\mathcal{A}$ is a simple separable
stable C*algebra with real rank zero, stable rank one, and
strict comparison of positive elements by traces, then whether
a positive element is a positive linear combination of projections
is determined by the trace values of its range projection.


On the notion of conductor in the local geometric Langlands correspondence Kamgarpour, Masoud Published: 20160602
Under the local Langlands correspondence, the conductor of an
irreducible representation of $\operatorname{Gl}_n(F)$ is greater than the
Swan conductor of the corresponding Galois representation. In
this paper, we establish the geometric analogue of this statement
by showing that the conductor of a categorical representation
of the loop group is greater than the irregularity of the corresponding
meromorphic connection.


Free function theory through matrix invariants Klep, Igor; Špenko, Špela Author's Draft
This paper concerns free function theory. Free maps are free
analogs of analytic functions in several complex variables,
and are defined in terms of freely noncommuting variables.
A function of $g$ noncommuting variables is a function on $g$tuples
of square matrices of all sizes that respects direct sums and
simultaneous conjugation.
Examples of such maps include noncommutative polynomials, noncommutative
rational functions and convergent noncommutative power series.


New deformations of convolution algebras and Fourier algebras on locally compact groups Lee, Hun Hee; Youn, Sanggyun Author's Draft
In this paper we introduce a new way of deforming convolution
algebras and Fourier algebras on locally compact groups. We demonstrate
that this new deformation allows us to reveal some information
of the underlying groups by examining Banach algebra properties
of deformed algebras. More precisely, we focus on representability
as an operator algebra of deformed convolution algebras on compact
connected Lie groups with connection to the real dimension of
the underlying group. Similarly, we investigate complete representability
as an operator algebra of deformed Fourier algebras on some finitely
generated discrete groups with connection to the growth rate
of the group.


On nonArchimedean curves omitting few components and their arithmetic analogues Levin, Aaron; Wang, Julie TzuYueh Published: 20150907
Let $\mathbf{k}$ be an algebraically closed field complete with respect
to a nonArchimedean absolute value of arbitrary characteristic.
Let $D_1,\dots, D_n$ be effective nef divisors intersecting
transversally in an $n$dimensional nonsingular projective variety
$X$.
We study the degeneracy of nonArchimedean analytic maps from
$\mathbf{k}$ into $X\setminus \cup_{i=1}^nD_i$ under various geometric
conditions. When $X$ is a rational ruled surface and $D_1$ and
$D_2$ are ample, we obtain a necessary and sufficient condition
such that
there is no nonArchimedean analytic map from $\mathbf{k}$ into $X\setminus
D_1 \cup D_2$.
Using the dictionary between nonArchimedean Nevanlinna theory
and Diophantine approximation that originated in
earlier work with T. T. H. An, %
we also study arithmetic analogues of these problems, establishing
results on integral points on these varieties over $\mathbb{Z}$
or the ring of integers of an imaginary quadratic field.


Onedimensional Schubert problems with respect to osculating flags Levinson, Jake Published: 20160719
We consider Schubert problems with respect to flags osculating
the rational normal curve. These problems are of special interest
when the osculation points are all real  in this case, for
zerodimensional Schubert problems, the solutions are "as real
as possible". Recent work by Speyer has extended the theory
to the moduli space
$
\overline{\mathcal{M}_{0,r}}
$,
allowing the points to collide.
These give rise to smooth covers of
$
\overline{\mathcal{M}_{0,r}}
(\mathbb{R})
$, with structure
and monodromy described by Young tableaux and jeu de taquin.


Isomorphisms of twisted Hilbert loop algebras Marquis, Timothée; Neeb, KarlHermann Published: 20160510
The closest infinite dimensional relatives of compact Lie algebras are HilbertLie algebras, i.e. real Hilbert spaces with a Lie
algebra
structure for which the scalar product is invariant.
Locally affine Lie algebras (LALAs)
correspond to double extensions of (twisted) loop algebras
over simple HilbertLie algebras $\mathfrak{k}$, also called
affinisations of $\mathfrak{k}$.
They possess a root space decomposition
whose corresponding root system is a locally affine root system
of one of the $7$ families $A_J^{(1)}$, $B_J^{(1)}$, $C_J^{(1)}$,
$D_J^{(1)}$, $B_J^{(2)}$, $C_J^{(2)}$ and $BC_J^{(2)}$ for some
infinite set $J$. To each of these types corresponds a ``minimal"
affinisation of some simple HilbertLie algebra $\mathfrak{k}$,
which we call standard.


On the digits of sumsets Mauduit, Christian; Rivat, Joël; Sárközy, András Published: 20160510
Let $\mathcal A$, $\mathcal B$ be large subsets of $\{1,\ldots,N\}$.
We study the number of pairs $(a,b)\in\mathcal A\times\mathcal B$ such that
the sum of binary digits of $a+b$ is fixed.


Mori's program for $\overline{M}_{0,7}$ with symmetric divisors Moon, HanBom Author's Draft
We complete Mori's program with symmetric divisors for the moduli
space of stable sevenpointed rational curves. We describe all
birational models in terms of explicit blowups and blowdowns.
We also give a moduli theoretic description of the first flip,
which has not appeared in the literature.


Extremal sequences for the Bellman function of the dyadic maximal operator and applications to the Hardy operator Nikolidakis, Eleftherios Nikolaos Published: 20160727
We prove that the extremal sequences for the
Bellman function of the dyadic maximal operator behave approximately
as eigenfunctions of this operator for a specific eigenvalue.
We use this result to prove the analogous one with respect to
the Hardy operator.


Almost disjointness preservers Oikhberg, Timur; Tradacete, Pedro Author's Draft
We study the stability of disjointness preservers on Banach lattices.
In many cases, we prove that an "almost disjointness preserving"
operator is well approximable by a disjointness preserving one.
However, this approximation is not always possible, as our
examples show.


Tannakian categories with semigroup actions Ovchinnikov, Alexey; Wibmer, Michael Author's Draft
Ostrowski's theorem implies that $\log(x),\log(x+1),\dots$ are
algebraically independent over $\mathbb{C}(x)$. More generally, for
a linear differential or difference equation, it is an important
problem to find all algebraic dependencies among a nonzero solution
$y$ and particular transformations of $y$, such as derivatives
of $y$ with respect to parameters, shifts of the arguments, rescaling,
etc. In the present paper, we develop a theory of Tannakian categories
with semigroup actions, which will be used to attack such questions
in full generality, as each linear differential equation gives
rise to a Tannakian category.
Deligne studied actions of braid groups on categories and obtained
a finite collection of axioms that characterizes such actions
to apply it to various geometric constructions. In this paper,
we find a finite set of axioms that characterizes actions of
semigroups that are finite free products of semigroups of the
form $\mathbb{N}^n\times
\mathbb{Z}/{n_1}\mathbb{Z}\times\cdots\times\mathbb{Z}/{n_r}\mathbb{Z}$
on Tannakian categories. This is the class of semigroups that
appear in many applications.


Optimal quotients of Jacobians with toric reduction and component groups Papikian, Mihran; Rabinoff, Joseph Published: 20160819
Let $J$ be a Jacobian variety with toric reduction
over a local field $K$.
Let $J \to E$ be an optimal quotient defined over $K$, where
$E$ is an elliptic curve.
We give examples in which the functorially induced map $\Phi_J
\to \Phi_E$
on component groups of the Néron models is not surjective.
This answers a question of Ribet and Takahashi.
We also give various criteria under which $\Phi_J \to \Phi_E$
is surjective, and discuss
when these criteria hold for the Jacobians of modular curves.


Global and non global solutions for some fractional heat equations with pure power nonlinearity Saanouni, Tarek Published: 20160621
The initial value problem for a semilinear fractional heat equation
is investigated. In the focusing case, global wellposedness
and exponential decay are obtained. In the focusing sign, global
and non global existence of solutions are discussed via the potential
well method.


The seven dimensional perfect Delaunay polytopes and Delaunay simplices Sikirić, Mathieu Dutour Published: 20160621
For a lattice $L$ of $\mathbb{RR}^n$, a sphere $S(c,r)$ of center $c$
and radius $r$
is called empty if for any $v\in L$ we have $\Vert v 
c\Vert \geq r$.
Then the set $S(c,r)\cap L$ is the vertex set of a {\em Delaunay
polytope}
$P=\operatorname{conv}(S(c,r)\cap L)$.
A Delaunay polytope is called {\em perfect} if any affine transformation
$\phi$ such that $\phi(P)$ is a Delaunay polytope is necessarily
an isometry
of the space composed with an homothety.


Anisotropic Sobolev Capacity with Fractional Order Xiao, Jie; Ye, Deping Published: 20160316
In this paper, we introduce the anisotropic
Sobolev capacity with fractional order and develop some basic
properties for this new object. Applications to the theory of
anisotropic fractional Sobolev spaces are provided. In particular,
we give geometric characterizations for a nonnegative Radon
measure $\mu$ that naturally induces an embedding of the anisotropic
fractional Sobolev class $\dot{\Lambda}_{\alpha,K}^{1,1}$ into
the $\mu$basedLebesguespace $L^{n/\beta}_\mu$ with $0\lt \beta\le
n$. Also, we investigate the anisotropic fractional $\alpha$perimeter.
Such a geometric quantity can be used to approximate the anisotropic
Sobolev capacity with fractional order. Estimation on the constant
in the related Minkowski inequality, which is asymptotically
optimal as $\alpha\rightarrow 0^+$, will be provided.


The ChernRicci flow on OeljeklausToma manifolds Zheng, Tao Published: 20160226
We study the ChernRicci flow, an evolution equation of Hermitian
metrics, on a family of OeljeklausToma (OT) manifolds which
are nonKähler compact complex manifolds with negative Kodaira
dimension. We prove that, after an initial conformal change,
the flow converges, in the
GromovHausdorff sense, to a torus with a flat Riemannian metric
determined by the OTmanifolds themselves.


La variante infinitésimale de la formule des traces de JacquetRallis pour les groupes unitaires Zydor, Michał Author's Draft
We establish an infinitesimal version of the
JacquetRallis trace formula for unitary groups.
Our formula is obtained by integrating a
truncated kernel à la Arthur.
It has a geometric side which is a
sum of distributions $J_{\mathfrak{o}}$ indexed by classes of
elements
of the Lie algebra of $U(n+1)$ stable by $U(n)$conjugation
as well as the "spectral side"
consisting of the Fourier transforms
of the aforementioned distributions.
We prove that the distributions $J_{\mathfrak{o}}$
are invariant and depend only on the choice of
the Haar measure on $U(n)(\mathbb{A})$.
For regular semisimple classes $\mathfrak{o}$, $J_{\mathfrak{o}}$
is
a relative orbital integral of JacquetRallis.
For classes $\mathfrak{o}$ called relatively regular semisimple,
we express $J_{\mathfrak{o}}$
in terms of relative orbital integrals regularised by means of
zêta functions.

