1. CJM 2014 (vol 66 pp. 1201)
 Adler, Jeffrey D.; Lansky, Joshua M.

Lifting Representations of Finite Reductive Groups I: Semisimple Conjugacy Classes
Suppose that $\tilde{G}$ is a connected reductive group
defined over a field $k$, and
$\Gamma$ is a finite group acting via $k$automorphisms
of $\tilde{G}$ satisfying a certain quasisemisimplicity condition.
Then the identity component of the group of $\Gamma$fixed points
in $\tilde{G}$ is reductive.
We axiomatize the main features of the relationship between this
fixedpoint group and the pair $(\tilde{G},\Gamma)$,
and consider any group $G$ satisfying the axioms.
If both $\tilde{G}$ and $G$ are $k$quasisplit, then we
can consider their duals $\tilde{G}^*$ and $G^*$.
We show the existence of and give an explicit formula for a natural
map from the set of semisimple stable conjugacy classes in $G^*(k)$
to the analogous set for $\tilde{G}^*(k)$.
If $k$ is finite, then our groups are automatically quasisplit,
and our result specializes to give a map
of semisimple conjugacy classes.
Since such classes parametrize packets of irreducible representations
of $G(k)$ and $\tilde{G}(k)$, one obtains a mapping of such packets.
Keywords:reductive group, lifting, conjugacy class, representation, Lusztig series Categories:20G15, 20G40, 20C33, 22E35 

2. CJM 2014 (vol 67 pp. 424)
 Samart, Detchat

Mahler Measures as Linear Combinations of $L$values of Multiple Modular Forms
We study the Mahler measures of certain families of Laurent
polynomials in two and three variables. Each of the known Mahler
measure formulas for these families involves $L$values of at most one
newform and/or at most one quadratic character. In this paper, we
show, either rigorously or numerically, that the Mahler measures of
some polynomials are related to $L$values of multiple newforms and
quadratic characters simultaneously. The results suggest that the
number of modular $L$values appearing in the formulas significantly
depends on the shape of the algebraic value of the parameter chosen
for each polynomial. As a consequence, we also obtain new formulas
relating special values of hypergeometric series evaluated at
algebraic numbers to special values of $L$functions.
Keywords:Mahler measures, EisensteinKronecker series, $L$functions, hypergeometric series Categories:11F67, 33C20 

3. CJM 2014 (vol 66 pp. 1078)
 Lanphier, Dominic; Skogman, Howard

Values of Twisted Tensor $L$functions of Automorphic Forms Over Imaginary Quadratic Fields
Let $K$ be a complex quadratic extension of $\mathbb{Q}$ and let $\mathbb{A}_K$
denote the adeles of $K$.
We find special values at all of the critical points of twisted
tensor $L$functions attached to cohomological cuspforms on $GL_2(\mathbb{A}_K)$,
and establish Galois equivariance of the values.
To investigate the values, we determine the archimedean factors
of a class of integral representations of these $L$functions,
thus proving a conjecture due to Ghate. We also investigate
analytic properties of these $L$functions, such as their functional
equations.
Keywords:twisted tensor $L$function, cuspform, hypergeometric series Categories:11F67, 11F37 

4. CJM 2013 (vol 66 pp. 284)
 Eikrem, Kjersti Solberg

Random Harmonic Functions in Growth Spaces and Blochtype Spaces
Let $h^\infty_v(\mathbf D)$ and $h^\infty_v(\mathbf B)$ be the spaces
of harmonic functions in the unit disk and multidimensional unit
ball
which admit a twosided radial majorant $v(r)$.
We consider functions $v $ that fulfill a doubling condition. In the
twodimensional case let $u (re^{i\theta},\xi) = \sum_{j=0}^\infty
(a_{j0} \xi_{j0} r^j \cos j\theta +a_{j1} \xi_{j1} r^j \sin j\theta)$
where $\xi =\{\xi_{ji}\}$ is a sequence of random
subnormal variables and $a_{ji}$ are
real; in higher dimensions we consider series of spherical harmonics.
We will obtain conditions on the coefficients $a_{ji} $ which imply
that $u$ is in $h^\infty_v(\mathbf B)$ almost surely.
Our estimate improves previous results by Bennett, Stegenga and
Timoney, and we prove that the estimate is sharp.
The results for growth spaces can easily be applied to Blochtype
spaces, and we obtain a similar characterization for these spaces,
which generalizes results by Anderson, Clunie and Pommerenke and by
Guo and Liu.
Keywords:harmonic functions, random series, growth space, Blochtype space Categories:30B20, 31B05, 30H30, 42B05 

5. CJM 2013 (vol 66 pp. 241)
 Broussous, P.

Transfert du pseudocoefficient de Kottwitz et formules de caractÃ¨re pour la sÃ©rie discrÃ¨te de $\mathrm{GL}(N)$ sur un corps local
Soit $G$ le groupe $\mathrm{GL}(N,F)$, oÃ¹ $F$ est un corps
localement compact et non archimÃ©dien.
En utilisant la thÃ©orie des types simples de Bushnell et Kutzko,
ainsi qu'une idÃ©e originale d'Henniart, nous construisons des pseudocoefficients
explicites pour les reprÃ©sentations de la sÃ©rie discrÃ¨te de $G$.
Comme application, nous en dÃ©duisons des formules
inÃ©dites pour la valeur du charactÃ¨re d'HarishChandra de certaines
telles reprÃ©sentations en certains Ã©lÃ©ments elliptiques
rÃ©guliers.
Keywords:reductive padic groups , discrete series, HarishChandra character, pseudocoefficient Category:22E50 

6. CJM 2012 (vol 65 pp. 241)
 Aguiar, Marcelo; Lauve, Aaron

Lagrange's Theorem for Hopf Monoids in Species
Following Radford's proof of Lagrange's theorem for pointed Hopf algebras,
we prove Lagrange's theorem for Hopf monoids in the category of
connected species.
As a corollary, we obtain necessary conditions for a given subspecies
$\mathbf k$ of a Hopf monoid $\mathbf h$ to be a Hopf submonoid: the quotient of
any one of the generating series of $\mathbf h$ by the corresponding
generating series of $\mathbf k$ must have nonnegative coefficients. Other
corollaries include a necessary condition for a sequence of
nonnegative integers to be the
dimension sequence of a Hopf monoid
in the form of certain polynomial inequalities, and of
a settheoretic Hopf monoid in the form of certain linear inequalities.
The latter express that the binomial transform of the sequence must be nonnegative.
Keywords:Hopf monoids, species, graded Hopf algebras, Lagrange's theorem, generating series, PoincarÃ©BirkhoffWitt theorem, Hopf kernel, Lie kernel, primitive element, partition, composition, linear order, cyclic order, derangement Categories:05A15, 05A20, 05E99, 16T05, 16T30, 18D10, 18D35 

7. CJM 2011 (vol 64 pp. 669)
 Pantano, Alessandra; Paul, Annegret; SalamancaRiba, Susana A.

The Genuine Omegaregular Unitary Dual of the Metaplectic Group
We classify all genuine unitary representations of the metaplectic group whose
infinitesimal character is real and at least as regular as that of the
oscillator representation. In a previous paper we exhibited a certain family
of representations satisfying these conditions, obtained by cohomological
induction from the tensor product of a onedimensional representation and an
oscillator representation. Our main theorem asserts that this family exhausts
the genuine omegaregular unitary dual of the metaplectic group.
Keywords:Metaplectic group, oscillator representation, bottom layer map, cohomological induction, Parthasarathy's Dirac Operator Inequality, pseudospherical principal series Category:22E46 

8. CJM 2011 (vol 64 pp. 935)
 McIntosh, Richard J.

The H and K Families of Mock Theta Functions
In his last letter to Hardy, Ramanujan
defined 17 functions $F(q)$, $q\lt 1$, which he called mock $\theta$functions.
He observed that as $q$ radially approaches any root of unity $\zeta$ at which
$F(q)$ has an exponential singularity, there is a $\theta$function
$T_\zeta(q)$ with $F(q)T_\zeta(q)=O(1)$. Since then, other functions have
been found that possess this property. These functions are related to
a function $H(x,q)$, where $x$ is usually $q^r$ or $e^{2\pi i r}$ for some
rational number $r$. For this reason we refer to $H$ as a ``universal'' mock
$\theta$function. Modular transformations of $H$ give rise to the functions
$K$, $K_1$, $K_2$. The functions $K$ and $K_1$ appear in Ramanujan's lost
notebook. We prove various linear relations between these functions using
AppellLerch sums (also called generalized Lambert series). Some relations
(mock theta ``conjectures'') involving mock $\theta$functions
of even order and $H$ are listed.
Keywords:mock theta function, $q$series, AppellLerch sum, generalized Lambert series Categories:11B65, 33D15 

9. CJM 2010 (vol 63 pp. 200)
 Rahman, Mizan

An Explicit Polynomial Expression for a $q$Analogue of the 9$j$ Symbols
Using standard transformation and summation formulas for basic
hypergeometric series we obtain an explicit polynomial form of the
$q$analogue of the 9$j$ symbols, introduced by the author in a
recent publication. We also consider a limiting case in which the
9$j$ symbol factors into two Hahn polynomials. The same
factorization occurs in another limit case of the corresponding
$q$analogue.
Keywords:6$j$ and 9$j$ symbols, $q$analogues, balanced and verywellpoised basic hypergeometric series, orthonormal polynomials in one and two variables, Racah and $q$Racah polynomials and their extensions Categories:33D45, 33D50 

10. CJM 2009 (vol 62 pp. 94)
11. CJM 2009 (vol 62 pp. 34)
 Campbell, Peter S.; Nevins, Monica

Branching Rules for Ramified Principal Series Representations of $\mathrm{GL}(3)$ over a $p$adic Field
We decompose the restriction of ramified principal series
representations of the $p$adic group $\mathrm{GL}(3,\mathrm{k})$ to its
maximal compact subgroup $K=\mathrm{GL}(3,R)$. Its decomposition is
dependent on the degree of ramification of the inducing characters and
can be characterized in terms of filtrations of the Iwahori subgroup
in $K$. We establish several irreducibility results and illustrate
the decomposition with some examples.
Keywords:principal series representations, branching rules, maximal compact subgroups, representations of $p$adic groups Categories:20G25, 20G05 

12. CJM 2007 (vol 59 pp. 673)
 Ash, Avner; Friedberg, Solomon

Hecke $L$Functions and the Distribution of Totally Positive Integers
Let $K$ be a totally real number field of degree $n$. We show that
the number of totally positive integers
(or more generally the number of totally positive elements of a given fractional ideal)
of given trace is evenly distributed around its expected value, which is
obtained from geometric considerations.
This result depends on unfolding an integral over
a compact torus.
Keywords:Eisenstein series, toroidal integral, Fourier series, Hecke $L$function, totally positive integer, trace Categories:11M41, 11F30, , 11F55, 11H06, 11R47 

13. CJM 2007 (vol 59 pp. 85)
 Foster, J. H.; Serbinowska, Monika

On the Convergence of a Class of Nearly Alternating Series
Let $C$ be the class of convex sequences of real numbers. The
quadratic irrational numbers can be partitioned into two types as
follows. If $\alpha$ is of the first type and $(c_k) \in C$, then
$\sum (1)^{\lfloor k\alpha \rfloor} c_k$ converges if and only if
$c_k \log k \rightarrow 0$. If $\alpha$ is of the second type and
$(c_k) \in C$, then $\sum (1)^{\lfloor k\alpha \rfloor} c_k$
converges if and only if $\sum c_k/k$ converges. An example of a
quadratic irrational of the first type is $\sqrt{2}$, and an
example of the second type is $\sqrt{3}$. The analysis of this
problem relies heavily on the representation of $ \alpha$ as a
simple continued fraction and on properties of the sequences of
partial sums $S(n)=\sum_{k=1}^n (1)^{\lfloor k\alpha \rfloor}$
and double partial sums $T(n)=\sum_{k=1}^n S(k)$.
Keywords:Series, convergence, almost alternating, convex, continued fractions Categories:40A05, 11A55, 11B83 

14. CJM 2000 (vol 52 pp. 961)
 Ismail, Mourad E. H.; Pitman, Jim

Algebraic Evaluations of Some Euler Integrals, Duplication Formulae for Appell's Hypergeometric Function $F_1$, and Brownian Variations
Explicit evaluations of the symmetric Euler integral $\int_0^1
u^{\alpha} (1u)^{\alpha} f(u) \,du$ are obtained for some particular
functions $f$. These evaluations are related to duplication formulae
for Appell's hypergeometric function $F_1$ which give reductions of
$F_1 (\alpha, \beta, \beta, 2 \alpha, y, z)$ in terms of more
elementary functions for arbitrary $\beta$ with $z = y/(y1)$ and for
$\beta = \alpha + \half$ with arbitrary $y$, $z$. These duplication
formulae generalize the evaluations of some symmetric Euler integrals
implied by the following result: if a standard Brownian bridge is
sampled at time $0$, time $1$, and at $n$ independent random times
with uniform distribution on $[0,1]$, then the broken line
approximation to the bridge obtained from these $n+2$ values has a
total variation whose mean square is $n(n+1)/(2n+1)$.
Keywords:Brownian bridge, Gauss's hypergeometric function, Lauricella's multiple hypergeometric series, uniform order statistics, Appell functions Categories:33C65, 60J65 

15. CJM 1998 (vol 50 pp. 794)
 Louboutin, Stéphane

Upper bounds on $L(1,\chi)$ and applications
We give upper bounds on the modulus of the values at $s=1$ of
Artin $L$functions of abelian extensions unramified at all
the infinite places. We also explain how we can compute better
upper bounds and explain how useful such computed bounds are
when dealing with class number problems for $\CM$fields. For
example, we will reduce the determination of all the
nonabelian normal $\CM$fields of degree $24$ with Galois
group $\SL_2(F_3)$ (the special linear group over the finite
field with three elements) which have class number one to the
computation of the class numbers of $23$ such $\CM$fields.
Keywords:Dedekind zeta function, Dirichlet series, $\CM$field, relative class number Categories:11M20, 11R42, 11Y35, 11R29 

16. CJM 1997 (vol 49 pp. 1224)
 Ørsted, Bent; Zhang, Genkai

Tensor products of analytic continuations of holomorphic discrete series
We give the irreducible decomposition
of the tensor product of an analytic continuation of
the holomorphic discrete
series of $\SU(2, 2)$ with its conjugate.
Keywords:Holomorphic discrete series, tensor product, spherical function, ClebschGordan coefficient, Plancherel theorem Categories:22E45, 43A85, 32M15, 33A65 

17. CJM 1997 (vol 49 pp. 543)
 Ismail, Mourad E. H.; Rahman, Mizan; Suslov, Sergei K.

Some summation theorems and transformations for $q$series
We introduce a double sum extension of a very wellpoised series and
extend to this the transformations of Bailey and Sears as well as the
${}_6\f_5$ summation formula of F.~H.~Jackson and the $q$Dixon sum.
We also give $q$integral representations of the double sum.
Generalizations of the NassrallahRahman integral are also found.
Keywords:Basic hypergeometric series, balanced series,, very wellpoised series, integral representations,, AlSalamChihara polynomials. Categories:33D20, 33D60 
