Automorphic period and the central value of Rankin-Selberg L-function

Wei Zhang

Type: Article

Publication Date: 2014-01-27

Citations: 75

DOI: https://doi.org/10.1090/s0894-0347-2014-00784-0

Abstract

We prove a refinement of the global Gan-Gross-Prasad conjecture proposed by Ichino-Ikeda and N. Harris for unitary groups under some local conditions. We need to assume some expected properties of L-packets and some part of the local Gan-Gross-Prasad conjecture.

Locations

Journal of the American Mathematical Society - View - PDF
arXiv (Cornell University) - View - PDF
DataCite API - View

Similar Works

Action	Title	Year	Authors
+	On the global Gan-Gross-Prasad conjecture for general spin groups	2018	Melissa Emory
+ PDF Chat	Refined global Gan–Gross–Prasad conjecture for Fourier–Jacobi periods on symplectic groups	2017	Hang Xue
+	Subconvexity for $L$-functions on ${\rm U}(n) \times {\rm U}(n+1)$ in the depth aspect	2023	Simon Marshall
+ PDF Chat	On the Periods of Automorphic Forms on Special Orthogonal Groups and the Gross–Prasad Conjecture	2009	Atsushi Ichino Tamutsu Ikeda
+ PDF Chat	The Gan-Gross-Prasad period of Klingen Eisenstein families over unitary groups	2024	R.F Xu
+	Anticyclotomic $p$-adic $L$-functions for Rankin--Selberg product	2023	Yifeng Liu
+	On the Non-vanishing of the Central Value of Certain L-functions: Unitary Groups	2018	Dihua Jiang Lei Zhang
+ PDF Chat	Fourier transform and the global Gan--Gross--Prasad conjecture for unitary groups	2014	Wei Zhang
+	Relative trace formulae and the Gan–Gross–Prasad conjectures	2023	Raphaël Beuzart-Plessis
+ PDF Chat	On the non-vanishing of the central value of certain $L$-functions: unitary groups	2020	Dihua Jiang Lei Zhang
+	The global Gan-Gross-Prasad conjecture for unitary groups. II. From Eisenstein series to Bessel periods	2023	Raphaël Beuzart-Plessis Pierre-Henri Chaudouard
+	The local Gan-Gross-Prasad conjecture for $U(n+1) \times U(n)$ : a non-generic case	2017	Jaeho Haan
+ PDF Chat	On the global Gan–Gross–Prasad conjecture for general spin groups	2020	Melissa Emory
+	Regularized periods and the global Gan–Gross–Prasad conjecture: the case of $$U(n+2r) \times U(n)$$	2023	Jaeho Haan
+	A Local Trace Formula for the Gan-gross-prasad Conjecture for Unitary Groups: The Archimedean Case	2020	Raphaël Beuzart-Plessis
+	Spectral reciprocity for $\mathrm{GL}(n)$ and simultaneous non-vanishing of central $L$-values	2021	Subhajit Jana Ramon M. Nunes
+	Spectral reciprocity for $\mathrm{GL}(n)$ and simultaneous non-vanishing of central $L$-values	2021	Subhajit Jana Ramon M. Nunes
+	Towards a $\mathrm{GL}_n$ variant of the Hoheisel phenomenon	2020	Peter Humphries Jesse Thorner
+	A local trace formula for the Gan-Gross-Prasad conjecture for unitary groups: the archimedean case	2015	Raphaël Beuzart-Plessis
+	The Refined Gross-Prasad Conjecture for Unitary Groups	2012	R. Neal Harris

Works That Cite This (75)

Action	Title	Year	Authors
+	Multiplicities and Plancherel formula for the space of nondegenerate Hermitian matrices.	2020	Raphaël Beuzart-Plessis
+ PDF Chat	On Deligne's conjecture for symmetric fourth L-functions of Hilbert modular forms	2023	Shih-Yu Chen
+ PDF Chat	BEYOND ENDOSCOPY FOR THE RELATIVE TRACE FORMULA II: GLOBAL THEORY	2017	Yiannis Sakellaridis
+	Special values of $L$-functions and the refined Gan-Gross-Prasad conjecture	2017	Harald Grobner Jie Lin
+	On central critical values of the degree four $$L$$ L -functions for $${\text {GSp}}\left( 4\right) $$ GSp 4 : a simple trace formula	2014	Masaaki Furusawa Kimball Martin
+ PDF Chat	Arithmetic diagonal cycles on unitary Shimura varieties	2020	Michael Rapoport Brian D. Smithling W. Zhang
+ PDF Chat	p-Adic and analytic properties of period integrals and values of L-functions	2016	Michael Harris
+	An Alternative Proof of Genericity for the Unitary Group in Three Variables	2016	Chongli Wang
+	Algebraicity of the near central non-critical value of symmetric fourth $L$-functions for Hilbert modular forms	2020	Shih-Yu Chen
+	Erratum to "On the Non-vanishing of the Central Value of the Rankin-Selberg L-functions"	2019	David Ginzburg Dihua Jiang Baiying Liu Stephen Rallis

Works Cited by This (53)

Action	Title	Year	Authors
+	On the nonnegativity of $L(\frac{1}{2},\pi)$ for ${\rm SO}_{2n+1}$	2003	Erez Lapid Stephen Rallis
+ PDF Chat	Archimedean Rankin-Selberg integrals	2009	Hervé Jacquet
+	Gross-Zagier Formula for GL(2), II	2004	Shou-Wu Zhang
+	Classical Fourier Analysis	2014	Loukas Grafakos
+ PDF Chat	Periods and harmonic analysis on spherical varieties	2018	Yiannis Sakellaridis Akshay Venkatesh
+	Models for certain residual representations of unitary groups	2009	David Ginzburg Dihua Jiang Stephen Rallis
+ PDF Chat	Twisted tensors and Euler products	1988	Yuval Z. Flicker
+	On the nonvanishing of the central value of the Rankin-Selberg 𝐿-functions	2004	David Ginzburg Dihua Jiang Stephen Rallis
+	On a conjecture of Jacquet	2001	Michael Harris Stephen S. Kudla
+	Tempered automorphic representations of the unitary group	2011	Paul-James White