Automorphic period and the central value of Rankin-Selberg L-function
نویسندگان
چکیده
منابع مشابه
The central value of the Rankin-Selberg L-functions
The values of L-functions at special points have been the subject of intensive studies. For example, a good positive lower bound for the central value of Hecke L-functions would rule out the existence of the Landau-Siegel zero, see the notable paper [IS]; the nonvanishing of certain Rankin-Selberg L-functions is a crucial ingredient in the current development of the generalized Ramanujan conjec...
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We recently established the holomorphic continuation and functional equation of the exterior square L-function for GL(n,Z), and more generally, the archimedean theory of the GL(n) exterior square L-function over Q. We refer the reader to our paper [15] for a precise statement of the results and their relation to previous work on the subject. The purpose of this note is to give an account of our...
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1.1. The refined Gan–Gross–Prasad conjecture. In this paper, as a sequel of [Xue14], we formulate a refinement to the global Gan–Gross–Prasad conjecture for the Fourier–Jacobi periods on U(n) × U(n) and prove it under some local conditions, assuming some expected properties of the L-packets and some parts of the local Gan–Gross–Prasad conjecture. This refinement is modeled on some recent work o...
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In this article we prove that given a holomorphic cusp form f and any point s0 in the complex plane, there is a holomorphic cusp form g such that the Rankin-Selberg L-function L(s, f × g) is non-zero at s0. Résumé: Dans cet article, on prouve le résultat suivant. Etat donné une forme holomorphe cuspidale f et un point quelquonque du plan complexe, il existe une forme holomorphe cuspidale g tell...
متن کاملOn the Exceptional Zeros of Rankin-selberg L-functions
In this paper we study the possibility of real zeros near s = 1 for the RankinSelberg L-functions L(s, f × g) and L(s, sym(g) × sym(g)), where f, g are newforms, holomorphic or otherwise, on the upper half plane H, and sym(g) denotes the automorphic form on GL(3)/Q associated to g by Gelbart and Jacquet ([GJ79]). We prove that the set of such zeros of these L-functions is the union of the corre...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2014
ISSN: 0894-0347,1088-6834
DOI: 10.1090/s0894-0347-2014-00784-0