Siegel modular forms and theta series attached to quaternion algebras

Siegfried Böcherer, Rainer Schulze‐Pillot

Type: Article

Publication Date: 1991-03-01

Citations: 76

DOI: https://doi.org/10.1017/s0027763000003391

Abstract

The two main problems in the theory of the theta correspondence or lifting (between automorphic forms on some adelic orthogonal group and on some adelic symplectic or metaplectic group) are the characterization of kernel and image of this correspondence. Both problems tend to be particularly difficult if the two groups are approximately the same size.

Locations

Nagoya Mathematical Journal - View - PDF
Project Euclid (Cornell University) - View - PDF

Similar Works

Action	Title	Year	Authors
+	Siegel Modular Forms and Theta Series attached to quaternion algebras II	1995	Siegfried Böcherer Rainer Schulze‐Pillot
+ PDF Chat	Siegel modular forms and theta series attached to quaternion algebras II	1997	Siegfried Böcherer Rainer Schulze‐Pillot
+	Siegel modular forms and theta series	1989	Siegfried Böcherer
+	THETA CORRESPONDENCE AND REPRESENTATION THEORY (Automorphic forms and representations of algebraic groups over local fields)	2003	享西山
+	THETA CORRESPONDENCE AND REPRESENTATION THEORY (Automorphic forms and representations of algebraic groups over local fields)	2003	Kyo Nishiyama
+	Siegel modular forms and theta series attached to quaternion algebras. II, With errata to: "Siegel modular forms and theta series attached to quaternion algebras''	1997	Siegfried Böcherer Rainer Schulze‐Pillot
+	Galois representations and theta operators for Siegel modular forms	2015	Angus McAndrew
+ PDF Chat	Quadratic Forms and Automorphic Forms	2013	Jonathan Hanke
+	Shimura correspondence for Maass wave forms and Selberg zeta functions (Automorphic forms and representations of algebraic groups over local fields)	2003	恒男荒川
+	Shimura correspondence for Maass wave forms and Selberg zeta functions (Automorphic forms and representations of algebraic groups over local fields)	2003	Tsuneo Arakawa
+ PDF Chat	The quaternionic Maass Spezialschar on split $\mathrm{SO}(8)$	2024	Jennifer Johnson-Leung Finn McGlade Isabella Negrini Aaron Pollack Manami Roy
+	Modular forms and Galois representations	2014	Takeshi Saito
+	EXPONENTIAL LIFTING AND HECKE CORRESPONDENCE(Researches on automorphic forms and zeta functions)	1997	Valeri A. Gritsenko
+	Representations of Galois Groups and Modular Forms	2000	Haruzo Hida
+	Galois representations and modular forms	2006	Takeshi Saito
+	Modular Forms and Galois Cohomology	2000	Haruzo Hida
+	Eisenstein series attached to lattices¶and modular forms on orthogonal groups	2001	Jan Hendrik Bruinier Michael Kuß
+	Introductory Lectures on Siegel Modular Forms	1990	Helmut Klingen
+	Galois representations for holomorphic Siegel modular forms	2012	Andrei Jorza
+ PDF Chat	Classical Theta Lifts for Higher Metaplectic Covering Groups	2020	Solomon Friedberg David Ginzburg

Works That Cite This (75)

Action	Title	Year	Authors
+ PDF Chat	On the Rankin–Selberg method for vector-valued Siegel modular forms	2020	Thanasis Bouganis Salvatore Mercuri
+ PDF Chat	Some Extensions of the Siegel-Weil Formula	2007	Stephen S. Kudla
+ PDF Chat	Bessel periods and the non-vanishing of Yoshida lifts modulo a prime	2016	Ming-Lun Hsieh Kenichi Namikawa
+	Yoshida lifts and the Bloch–Kato conjecture for the convolution L -function	2013	Mahesh Agarwal Krzysztof Klosin
+ PDF Chat	Siegel Modular Forms of Genus 2 and Level 2: Cohomological Computations and Conjectures	2008	Jonas Bergström Carel Faber Gerard van der Geer
+ PDF Chat	Semistable Abelian Varieties with Small Division Fields	2004	Armand Brumer Kenneth Kramer
+	Congruences modulo 2 for dimensions of spaces of cusp forms	2014	Satoshi Wakatsuki
+ PDF Chat	A mean value of a triple product of L-functions	2016	Jack Buttcane Rizwanur Khan
+ PDF Chat	Nearly holomorphic automorphic forms on Sp2n with sufficiently regular infinitesimal characters and applications	2022	Shuji Horinaga
+ PDF Chat	Siegel modular forms and theta series attached to quaternion algebras II	1997	Siegfried Böcherer Rainer Schulze‐Pillot

Works Cited by This (60)

Action	Title	Year	Authors
+	Automorphic forms on Adele groups	1975	Stephen Gelbart
+	Zur Zahlentheorie der Quaternionen-Algebren.	1955	Martin Eichler
+ PDF Chat	Construction of siegel modular forms of degree three and commutation relations of Hecke operators	1985	Yoshio Tanigawa
+ PDF Chat	Representations of quadratic forms and their application to Selberg’s zeta functions	1976	Yoshiyuki Kitaoka
+ PDF Chat	Singular Modular Forms and Theta Relations	1991	Eberhard Freitag
+ PDF Chat	Dirichlet series in the theory of Siegel modular forms	1984	Yoshiyuki Kitaoka
+	Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains	1963	Hua Li
+	Quadratische Formen und orthogonale Gruppen	1974	Martin Eichler
+	On the howe duality conjecture	1984	Stephen Rallis
+ PDF Chat	Arithmétique des Algèbres de Quaternions	1980	Marie-France Vignéras