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There is reason to expe
t that the 2k-th moment of the Riemann zeta
fun
tion
an be related to the spe
tral theory of GL(k) or GL(2k). The work
of Motohashi [27℄ supports the idea of seeki...
With this assumption, we now work with u1 = u2 = 0 and use only u3. By the extension to o of
Dirichlet's theorem on primes in an arithmetic progression, we may nd u3 such that C
1 = C1+u3A1
is pr...
Gauss Sum Combinatorics and Metaplectic Eisenstein Series
Metaplectic Eisenstein Series Gauss Sum Combinatorics
2015/7/6
For metaplectic covers of these groups, the Whittaker models may or may not be
unique. Gelbart and Piatetski-Shapiro considered the representations of the double
cover of SL2 that have unique Whitta...
Weyl Group Multiple Dirichlet Series, Eisenstein Series and Crystal Bases
Eisenstein Series Crystal Bases
2015/7/6
If F is a local eld containing the group n of n-th roots of unity, and if G is a split
semisimple simply connected algebraic group, then Matsumoto [27] de ned an n-fold
covering group of G(F), tha...
Automorphic forms are generalizations of periodic functions; they are functions on a group that
are invariant under a discrete subgroup. A natural way to arrange this invariance is by averaging.
Eis...
We de ne Schubert Eisenstein series as sums like usual Eisenstein
series but with the summation restricted to elements of a particular Schubert
cell, indexed by an element of the Weyl group. They ar...
Semi-ordinary p-stabilization of the Siegel Eisenstein series of arbitrary genus
Siegel modular forms Eisenstein series p-adic analytic family
2012/7/11
For a given odd prime p, we define a certain p-stabilization of the Siegel Eisenstein series of arbitrary genus so that the resulting eigenvalue of a generalized Atkin operator at p is a p-adic unit (...
On higher congruences between cusp forms and Eisenstein series
higher congruences cusp forms Eisenstein series Number Theory
2012/6/30
In this paper we present several finite families of congruences between cusp forms and Eisenstein series of higher weights at powers of prime ideals. We formulate a conjecture which describes properti...
Equidistribution of Eisenstein series on convex co-compact hyperbolic manifolds
Equidistribution of Eisenstein series convex co-compact hyperbolic manifolds Spectral Theory
2011/9/5
Abstract: For convex co-compact hyperbolic manifolds $\Gamma\backslash \mathbb{H}^{n+1}$ for which the dimension of the limit set satisfies $\delta_\Gamma< n/2$, we show that the high-frequency Eisens...
Non-abelian $p$-adic $L$-functions and Eisenstein series of unitary groups; the CM method
Eisenstein series unitary groups the CM method Number Theory
2011/8/26
Abstract: In this work we prove the so-called "torsion congruences" between abelian $p$-adic $L$-functions that are related to automorphic representations of definite unitary groups. These congruences...
Eisenstein Series, Alternative Modular Bases and Approximations of $1/\pi$
Eisenstein Series Alternative Modular Bases
2010/11/22
In this article using the theory of Eisenstein series, we give rise to the complete evaluation of two Gauss hypergeometric functions. Moreover we evaluate the modulus of each of these functions and t...
Pullbacks of Siegel Eisenstein Series and Weighted Averages of Critical $L$-values
Special values of L-functions pullbacks of Eisenstein series
2010/11/29
In this paper we obtain a weighted average formula for special values of L-functions attached to normalized elliptic modular forms of weight k and full level. These results are obtained by studying th...
The elliptic curve in the S-duality theory and Eisenstein series for Kac-Moody groups
elliptic curve S-duality theory Eisenstein series Kac-Moody groups
2010/10/29
We establish a relation between the generating functions appearing in the S-duality conjecture of Vafa and Witten and geometric Eisenstein series for Kac-Moody groups. For a pair consisting of a surfa...