Rallis, Stephen 1942
Overview
Works:  24 works in 84 publications in 3 languages and 2,225 library holdings 

Genres:  Conference proceedings 
Roles:  Author, Editor 
Classifications:  QA246, 515.9 
Publication Timeline
.
Most widely held works by
Stephen Rallis
The descent map from automorphic representations of GL to classical groups
by
D Ginzburg(
)
13 editions published between 2010 and 2011 in English and held by 692 WorldCat member libraries worldwide
This book introduces the method of automorphic descent, providing an explicit inverse map to the (weak) Langlands functorial lift from generic, cuspidal representations on classical groups to general linear groups. The essence of this method is the study of certain Fourier coefficients of GelfandGraev type, or of FourierJacobi type when applied to certain residual Eisenstein series. This book contains a complete account of this automorphic descent, with complete, detailed proofs. The book will be of interest to graduate students and mathematicians, who specialize in automorphic forms and in representation theory of reductive groups over local fields. Relatively selfcontained, the content of some of the chapters can serve as topics for graduate students seminars
13 editions published between 2010 and 2011 in English and held by 692 WorldCat member libraries worldwide
This book introduces the method of automorphic descent, providing an explicit inverse map to the (weak) Langlands functorial lift from generic, cuspidal representations on classical groups to general linear groups. The essence of this method is the study of certain Fourier coefficients of GelfandGraev type, or of FourierJacobi type when applied to certain residual Eisenstein series. This book contains a complete account of this automorphic descent, with complete, detailed proofs. The book will be of interest to graduate students and mathematicians, who specialize in automorphic forms and in representation theory of reductive groups over local fields. Relatively selfcontained, the content of some of the chapters can serve as topics for graduate students seminars
Lfunctions and the oscillator representation
by
Stephen Rallis(
Book
)
12 editions published in 1987 in English and German and held by 475 WorldCat member libraries worldwide
These notes are concerned with showing the relation between Lfunctions of classical groups (*F1 in particular) and *F2 functions arising from the oscillator representation of the dual reductive pair *F1 *F3 O(Q). The problem of measuring the nonvanishing of a *F2 correspondence by computing the Petersson inner product of a *F2 lift from *F1 to O(Q) is considered. This product can be expressed as the special value of an Lfunction (associated to the standard representation of the Lgroup of *F1) times a finite number of local Euler factors (measuring whether a given local representation occurs in a given oscillator representation). The key ideas used in proving this are (i) new Rankin integral representations of standard Lfunctions, (ii) seesaw dual reductive pairs and (iii) SiegelWeil formula. The book addresses readers who specialize in the theory of automorphic forms and Lfunctions and the representation theory of Lie groups. N
12 editions published in 1987 in English and German and held by 475 WorldCat member libraries worldwide
These notes are concerned with showing the relation between Lfunctions of classical groups (*F1 in particular) and *F2 functions arising from the oscillator representation of the dual reductive pair *F1 *F3 O(Q). The problem of measuring the nonvanishing of a *F2 correspondence by computing the Petersson inner product of a *F2 lift from *F1 to O(Q) is considered. This product can be expressed as the special value of an Lfunction (associated to the standard representation of the Lgroup of *F1) times a finite number of local Euler factors (measuring whether a given local representation occurs in a given oscillator representation). The key ideas used in proving this are (i) new Rankin integral representations of standard Lfunctions, (ii) seesaw dual reductive pairs and (iii) SiegelWeil formula. The book addresses readers who specialize in the theory of automorphic forms and Lfunctions and the representation theory of Lie groups. N
Explicit constructions of automorphic Lfunctions
by
Stephen S Gelbart(
Book
)
14 editions published in 1987 in English and German and held by 469 WorldCat member libraries worldwide
The goal of this research monograph is to derive the analytic continuation and functional equation of the Lfunctions attached by R.P. Langlands to automorphic representations of reductive algebraic groups. The first part of the book (by PiatetskiShapiro and Rallis) deals with Lfunctions for the simple classical groups; the second part (by Gelbart and PiatetskiShapiro) deals with nonsimple groups of the form G GL(n), with G a quasisplit reductive group of split rank n. The method of proof is to construct certain explicit zetaintegrals of RankinSelberg type which interpolate the relevant Langlands Lfunctions and can be analyzed via the theory of Eisenstein series and intertwining operators. This is the first time such an approach has been applied to such general classes of groups. The flavor of the local theory is decidedly representation theoretic, and the work should be of interest to researchers in group representation theory as well as number theory
14 editions published in 1987 in English and German and held by 469 WorldCat member libraries worldwide
The goal of this research monograph is to derive the analytic continuation and functional equation of the Lfunctions attached by R.P. Langlands to automorphic representations of reductive algebraic groups. The first part of the book (by PiatetskiShapiro and Rallis) deals with Lfunctions for the simple classical groups; the second part (by Gelbart and PiatetskiShapiro) deals with nonsimple groups of the form G GL(n), with G a quasisplit reductive group of split rank n. The method of proof is to construct certain explicit zetaintegrals of RankinSelberg type which interpolate the relevant Langlands Lfunctions and can be analyzed via the theory of Eisenstein series and intertwining operators. This is the first time such an approach has been applied to such general classes of groups. The flavor of the local theory is decidedly representation theoretic, and the work should be of interest to researchers in group representation theory as well as number theory
L functions for the orthogonal group
by
D Ginzburg(
Book
)
10 editions published in 1997 in English and held by 238 WorldCat member libraries worldwide
10 editions published in 1997 in English and held by 238 WorldCat member libraries worldwide
Weil representation I : intertwining distributions and discrete spectrum
by
Stephen Rallis(
Book
)
10 editions published in 1980 in English and held by 201 WorldCat member libraries worldwide
10 editions published in 1980 in English and held by 201 WorldCat member libraries worldwide
Automorphic representations, Lfunctions and applications : progress and prospects : proceedings of a conference honoring Steve Rallis on the occasion of his 60th birthday, the Ohio State University, March 2730, 2003
(
Book
)
1 edition published in 2005 in English and held by 73 WorldCat member libraries worldwide
Review text: "This volume should be of interest both to researchers and students in the area of automorphic representations, as well as to mathematicians in other areas interested in having an overview of current developments in this important field."L'Enseignement Mathematique 34/2005
1 edition published in 2005 in English and held by 73 WorldCat member libraries worldwide
Review text: "This volume should be of interest both to researchers and students in the area of automorphic representations, as well as to mathematicians in other areas interested in having an overview of current developments in this important field."L'Enseignement Mathematique 34/2005
Méthodes mathématiques pour calculateurs arithmétiques
by
Anthony Ralston(
Book
)
1 edition published in 1965 in French and held by 19 WorldCat member libraries worldwide
1 edition published in 1965 in French and held by 19 WorldCat member libraries worldwide
Weil representation
by
Stephen Rallis(
Book
)
1 edition published in 1980 in English and held by 13 WorldCat member libraries worldwide
1 edition published in 1980 in English and held by 13 WorldCat member libraries worldwide
Weil representation
by
Stephen Rallis(
Book
)
5 editions published in 1980 in English and Undetermined and held by 11 WorldCat member libraries worldwide
5 editions published in 1980 in English and Undetermined and held by 11 WorldCat member libraries worldwide
Automorphic forms constructed from the weil representation, holomorphic case
by
Stephen Rallis(
Book
)
1 edition published in 1976 in English and held by 7 WorldCat member libraries worldwide
1 edition published in 1976 in English and held by 7 WorldCat member libraries worldwide
The orbit and th correspondence for some dual pairs
by
Stephen Rallis(
Book
)
2 editions published in 1993 in French and English and held by 5 WorldCat member libraries worldwide
2 editions published in 1993 in French and English and held by 5 WorldCat member libraries worldwide
Weil representation
by
Stephen Rallis(
Book
)
1 edition published in 1974 in German and held by 4 WorldCat member libraries worldwide
1 edition published in 1974 in German and held by 4 WorldCat member libraries worldwide
Intertwining distributions and discrete spectrum
by
Stephen Rallis(
Book
)
1 edition published in 1980 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 1980 in English and held by 4 WorldCat member libraries worldwide
Automorphic Cusp forms constructed from the Weil representation
by
Stephen Rallis(
Book
)
2 editions published between 1976 and 1979 in English and held by 3 WorldCat member libraries worldwide
2 editions published between 1976 and 1979 in English and held by 3 WorldCat member libraries worldwide
Lfunctions and oscillator representation
by
Stephen Rallis(
)
1 edition published in 1987 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1987 in English and held by 2 WorldCat member libraries worldwide
Discrete spectrum of Weil representation
by
Stephen Rallis(
Book
)
1 edition published in 1976 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1976 in English and held by 2 WorldCat member libraries worldwide
Représentations
by
Stephen Rallis(
Book
)
1 edition published in 1976 in French and held by 2 WorldCat member libraries worldwide
1 edition published in 1976 in French and held by 2 WorldCat member libraries worldwide
Répresentations supercuspidales du groupe metaplectique
by
Stephen Rallis(
Book
)
1 edition published in 1979 in French and held by 1 WorldCat member library worldwide
1 edition published in 1979 in French and held by 1 WorldCat member library worldwide
Weil representation, 1 : Intertwining distributions
by
Stephen Rallis(
Book
)
1 edition published in 1974 in English and held by 1 WorldCat member library worldwide
1 edition published in 1974 in English and held by 1 WorldCat member library worldwide
On the Howe duality conjecture
(
)
1 edition published in 1984 in English and held by 1 WorldCat member library worldwide
1 edition published in 1984 in English and held by 1 WorldCat member library worldwide
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Related Identities
 Ginzburg, D. (David) Author
 Pi︠a︡tet︠s︡kiĭShapiro, I. I. (Ilʹi︠a︡ Iosifovich) 19292009
 Soudry, David 1956 Author
 Gelbart, Stephen S. 1946 Author
 Schiffmann, Gerard 1940
 Cogdell, James W. 1953
 SpringerLink (Service en ligne)
 Wilf, Herbert S. 1931 Editor
 Piatetskishapiro, I.
 American Mathematical Society