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241  Multiple ZetaFunctions Associated with Linear Recurrence Sequences and the Vectorial Sum Formula Essouabri, Driss; Matsumoto, Kohji; Tsumura, Hirofumi
We prove the holomorphic continuation of certain multivariable multiple
zetafunctions whose coefficients satisfy a suitable recurrence condition.
In fact, we introduce more general vectorial zetafunctions and prove their
holomorphic continuation. Moreover, we show a vectorial sum formula among
those vectorial zetafunctions from which some generalizations of the
classical sum formula can be deduced.


277  Locally Indecomposable Galois Representations Ghate, Eknath; Vatsal, Vinayak
In a previous paper
the authors showed that, under some technical
conditions,
the local Galois representations attached to the members of
a nonCM family of ordinary cusp forms are indecomposable for all
except possibly finitely many
members of the family. In this paper we use deformation theoretic
methods to give examples of nonCM families for
which every classical member of weight at least two has a locally
indecomposable Galois representation.


298  A Variant of Lehmer's Conjecture, II: The CMcase Gun, Sanoli; Murty, V. Kumar
Let $f$ be a normalized Hecke eigenform with rational integer Fourier
coefficients. It is an interesting question to know how often an
integer $n$ has a factor common with the $n$th Fourier coefficient of
$f$. It has been shown in previous papers that this happens very often. In this
paper, we give an asymptotic formula for the number of integers $n$
for which $(n, a(n)) = 1$, where $a(n)$ is the $n$th Fourier coefficient of
a normalized Hecke eigenform $f$ of weight $2$ with rational integer
Fourier coefficients and having complex multiplication.


327  Discrete Series for $p$adic $SO(2n)$ and Restrictions of Representations of $O(2n)$ Jantzen, Chris
In this paper we give a classification of discrete series for
$SO(2n,F)$, $F$ $p$adic, similar to that of
MœglinTadić for
the other classical groups. This is obtained by taking the
MœglinTadić classification for $O(2n,F)$ and studying how the
representations restrict to $SO(2n,F)$. We then extend this to an
analysis of how admissible representations of $O(2n,F)$ restrict.


381  A Complete Classification of AI Algebras with the Ideal Property Ji, Kui ; Jiang, Chunlan
Let $A$ be an AI algebra; that is, $A$ is the $\mbox{C}^{*}$algebra inductive limit
of a sequence
$$
A_{1}\stackrel{\phi_{1,2}}{\longrightarrow}A_{2}\stackrel{\phi_{2,3}}{\longrightarrow}A_{3}
\longrightarrow\cdots\longrightarrow A_{n}\longrightarrow\cdots,
$$
where
$A_{n}=\bigoplus_{i=1}^{k_n}M_{[n,i]}(C(X^{i}_n))$,
$X^{i}_n$ are $[0,1]$, $k_n$, and
$[n,i]$ are positive integers.
Suppose that $A$ has the
ideal property: each closed twosided ideal of $A$ is generated by
the projections inside the ideal, as a closed twosided ideal.
In this article, we give a complete classification of AI algebras with the ideal property.


413  Generating Functions for Hecke Algebra Characters Konvalinka, Matjaž; Skandera, Mark
Certain polynomials in $n^2$ variables that serve as generating
functions for symmetric group characters are sometimes called
($S_n$) character immanants.
We point out a close connection between the identities of
LittlewoodMerrisWatkins
and GouldenJackson, which relate $S_n$ character immanants
to the determinant, the permanent and MacMahon's Master Theorem.
From these results we obtain a generalization
of Muir's identity.
Working with the quantum polynomial ring and the Hecke algebra
$H_n(q)$, we define quantum immanants that are generating
functions for Hecke algebra characters.
We then prove quantum analogs of the LittlewoodMerrisWatkins identities
and selected GouldenJackson identities
that relate $H_n(q)$ character immanants to
the quantum determinant, quantum permanent, and quantum Master Theorem
of GaroufalidisL\^eZeilberger.
We also obtain a generalization of Zhang's quantization of Muir's
identity.


436  Simplicial Complexes and Open Subsets of NonSeparable LFSpaces Mine, Kotaro; Sakai, Katsuro
Let $F$ be a nonseparable LFspace homeomorphic to
the direct sum $\sum_{n\in\mathbb{N}} \ell_2(\tau_n)$,
where $\aleph_0 < \tau_1 < \tau_2 < \cdots$.
It is proved that
every open subset $U$ of $F$ is homeomorphic to the product $K \times F$
for some locally finitedimensional simplicial complex $K$ such that
every vertex $v \in K^{(0)}$ has the star $\operatorname{St}(v,K)$
with $\operatorname{card} \operatorname{St}(v,K)^{(0)} < \tau = \sup\tau_n$
(and $\operatorname{card} K^{(0)} \le \tau$),
and, conversely, if $K$ is such a simplicial complex,
then the product $K \times F$ can be embedded in $F$ as an open set,
where $K$ is the polyhedron of $K$ with the metric topology.


460  Monotonically Controlled Mappings Pavlíček, Libor
We study classes of mappings between finite and infinite dimensional
Banach spaces that are monotone and mappings which are differences
of monotone mappings (DM). We prove a RadóReichelderfer estimate
for monotone mappings in finite dimensional spaces that remains
valid for DM mappings. This provides an alternative proof of the
Fréchet differentiability a.e. of DM mappings. We establish a
Morreytype estimate for the distributional derivative of monotone
mappings. We prove that a locally DM mapping between finite
dimensional spaces is also globally DM. We introduce and study a new
class of the socalled UDM mappings between Banach spaces, which
generalizes the concept of curves of finite variation.
