Kloosterman identities over a quadratic extension II

H. Jacquet

Type: Article

Publication Date: 2005-07-01

Citations: 17

DOI: https://doi.org/10.1016/j.ansens.2005.05.001

Abstract

Abstract We prove certain identities between Kloosterman integrals. They constitute the fundamental lemma of a relative trace formula for Hecke functions. The main application of the trace formula in question is the following result. Let E / F be a quadratic extension of number fields. A cuspidal automorphic representation of GL ( n , E A ) is distinguished by some unitary group if and only if it is the base change of an automorphic cuspidal representation of GL ( n , F A ) .

Locations

Annales Scientifiques de l École Normale Supérieure - View
French digital mathematics library (Numdam) - View - PDF

Similar Works

Action	Title	Year	Authors
+ PDF Chat	On a Generalization of a Result of Waldspurger	1996	Jiandong Guo
+ PDF Chat	Relative Kloosterman Integrals For Gl(3): III	1993	Zhengyu Mao
+	Twisted relative trace formulae with a view towards unitary groups	2017	Jayce R. Getz Eric Wambach
+ PDF Chat	A relative trace formula proof of the Petersson trace formula	2006	Andrew Knightly Charles Li
+ PDF Chat	Kloosterman integrals for skew symmetric matrices	1992	Hervé Jacquet Stephen Rallis
+	Twisted relative trace formulae with a view towards unitary groups	2017	Jayce R. Getz Eric Wambach
+	On L-functions for U2+1 × Res/GL (m > n)	2020	Kazuki Morimoto David Soudry
+	Exponential Sums forGL(n) and Their Applications to Base Change	1998	Ye Yangbo
+	None	1998	Yangbo Ye
+ PDF Chat	Twisted relative trace formulae with a view towards unitary groups	2014	Jayce R. Getz Eric Wambach
+	Isolating Rankin-Selberg lifts	2015	Jayce R. Getz Jamie Klassen
+ PDF Chat	Relative Kloosterman Integrals for GL(3): II	1992	Hervé Jacquet
+	Local Orbital Integrals of a Relative Trace Formula	1993	叶扬波
+ PDF Chat	Eisenstein Series and the Selberg Trace Formula. II	1987	H. Jacquet D. Zagier
+ PDF Chat	Kloosterman identities over a quadratic extension	2004	Hervé Jacquet
+	A spectral expansion for the symmetric space $\mathrm{GL}_n(E)/\mathrm{GL}_n(F)$	2022	Pierre-Henri Chaudouard
+	Comparing Hecke Coefficients of Automorphic Representations	2018	Liubomir Chiriac Andrei Jorza
+ PDF Chat	Trace formulae and applications to class numbers	2014	Nicole Raulf
+ PDF Chat	Distinguished representations for unitary groups	1997	Ramanujachary Kumanduri
+	A note on the trace formula	2023	Eran Assaf

Works That Cite This (17)

Action	Title	Year	Authors
+ PDF Chat	Lower bounds for Maass forms on semisimple groups	2020	Farrell Brumley Simon Marshall
+ PDF Chat	Compact unitary periods	2007	Erez Lapid Omer Offen
+ PDF Chat	Multiplicities and Plancherel formula for the space of nondegenerate Hermitian matrices	2021	Raphaël Beuzart-Plessis
+ PDF Chat	A remark on the fundamental lemma of Jacquet	2006	Omer Offen
+ PDF Chat	Twisted relative trace formulae with a view towards unitary groups	2014	Jayce R. Getz Eric Wambach
+ PDF Chat	Smooth transfer of Kloosterman integrals (the Archimedean case)	2013	Avraham Aizenbud Dmitry Gourevitch
+ PDF Chat	Kloosterman integrals for GL(2,R)	2005	Hervé Jacquet
+ PDF Chat	A fundamental lemma for the Hecke algebra: The Jacquet–Rallis case	2022	Spencer Leslie
+ PDF Chat	On representations distinguished by unitary groups	2012	Brooke Feigon Erez Lapid Omer Offen
+	Supercuspidal representations of $\mathrm{GL}_{n}(F)$ distinguished by a unitary involution	2019	Jiandi Zou

Works Cited by This (26)

Action	Title	Year	Authors
+	Representations and invariants of the classical groups	1998	Roe Goodman Nolan R. Wallach
+	Le lemme fondamental de Jacquet et Ye en caractéristique positive	1999	Báo Châu Ngô
+ PDF Chat	Symmetric Functions and Orthogonal Polynomials	1997	I. Macdonald
+ PDF Chat	Germs of Kloosterman Integrals for $GL(3)$	1999	Hervé Jacquet Yangbo Ye
+	Kloosterman integrals and base change for GL (2).	1989	Yangbo Ye
+ PDF Chat	Distinguished representations and quadratic base change for 𝐺𝐿(3)	1996	Hervé Jacquet Yangbo Ye
+ PDF Chat	Faisceaux pervers, homomorphisme de changement de base et lemme fondamental de jacquet et ye	1999	B. C. Ngô
+ PDF Chat	Kloosterman integrals for skew symmetric matrices	1992	Hervé Jacquet Stephen Rallis
+	Factorization of Period Integrals	2001	Hervé Jacquet
+ PDF Chat	Transfert lisse d'intégrales de Kloosterman	2002	Hervé Jacquet