Results 11 to 20 of about 265 (42)
Period integrals and Rankin-Selberg L-functions on GL(n) [PDF]
, 2011 We compute the second moment of a certain family of Rankin-Selberg $L$-functions L(f x g, 1/2) where f and g are Hecke-Maass cusp forms on GL(n). Our bound is as strong as the Lindel\"of hypothesis on average, and recovers individually the convexity ...
Blomer, Valentin
core +2 more sources
Determination of $GL(3)$ Hecke-Maass forms from twisted central values [PDF]
, 2014 Suppose $\pi_1$ and $\pi_2$ are two Hecke-Maass cusp forms for $SL(3,\mathbb{Z})$ such that for all primitive character $\chi$ we have $$ L(\tfrac{1}{2},\pi_1\otimes\chi)=L(\tfrac{1}{2},\pi_2\otimes\chi). $$ Then we show that $\pi_1=\pi_2$.Comment: First
Munshi, Ritabrata, Sengupta, Jyoti
core +1 more source
Dirichlet series of Rankin-Cohen Brackets [PDF]
, 2010 Given modular forms $f$ and $g$ of weights $k$ and $\ell$, respectively, their Rankin-Cohen bracket $[f,g]^{(k, \ell)}_n$ corresponding to a nonnegative integer $n$ is a modular form of weight $k +\ell +2n$, and it is given as a linear combination of the
Choie, YongJu, Lee, Min Ho
core +2 more sources
On mean values of some zeta-functions in the critical strip [PDF]
, 2003 For a fixed integer $k\ge 3$ and fixed $1/2 1$ we consider $$ \int_1^T |\zeta(\sigma + it)|^{2k}dt = \sum_{n=1}^\infty d_k^2(n)n^{-2\sigma}T + R(k,\sigma;T), $$ where $R(k,\sigma;T) = o(T) (T\to\infty)$ is the error term in the above asymptotic formula.
Ivić, Aleksandar
core +2 more sources
Uniform approximate functional equation for principal L-functions
, 2002 We prove an approximate functional equation for the central value of the L-series attached to an irreducible cuspidal automorphic representation of GL(m) over a number field with unitary central character.
Harcos, Gergely
core +1 more source
Eisenstein Cohomology and ratios of critical values of Rankin-Selberg L-functions
, 2011 This is an announcement of results on rank-one Eisenstein cohomology of GL(N), with N > 1 an odd integer, and algebraicity theorems for ratios of successive critical values of certain Rankin-Selberg L-functions for GL(n) x GL(n') when n is even and n' is
Harder, Guenter, Raghuram, A.
core +1 more source
Doubling constructions and tensor product L-functions: coverings of the symplectic group
Forum of Mathematics, SigmaIn this work, we develop an integral representation for the partial L-function of a pair $\pi \times \tau $ of genuine irreducible cuspidal automorphic representations, $\pi $ of the m-fold covering of Matsumoto of the symplectic group $
Eyal Kaplan
doaj +1 more source
On a convolution series attached to a Siegel Hecke cusp form of degree 2
, 2013 We prove that the "naive" convolution Dirichlet series D_2(s) attached to a degree 2 Siegel Hecke cusp form F, has a pole at s=1. As an application, we write down the asymptotic formula for the partial sums of the squares of the eigenvalues of $F$ with ...
Das, Soumya +2 more
core +1 more source
Quasi-polynomial representations of double affine Hecke algebras
Forum of Mathematics, SigmaWe introduce an explicit family of representations of the double affine Hecke algebra $\mathbb {H}$ acting on spaces of quasi-polynomials, defined in terms of truncated Demazure-Lusztig type operators.
Siddhartha Sahi +2 more
doaj +1 more source
Non-vanishing of $L$-functions associated to cusp forms of half-integral weight
, 2013 In this article, we prove non-vanishing results for $L$-functions associated to holomorphic cusp forms of half-integral weight on average (over an orthogonal basis of Hecke eigenforms). This extends a result of W.
G. Shimura +7 more
core +1 more source