WorldCat Identities

Rallis, Stephen 1942-

Overview
Works: 19 works in 94 publications in 3 languages and 2,704 library holdings
Genres: Conference papers and proceedings 
Roles: Author, Editor
Classifications: QA3, 515.9
Publication Timeline
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Most widely held works by Stephen Rallis
Explicit constructions of automorphic L-functions by Stephen S Gelbart( Book )

16 editions published in 1987 in English and German and held by 390 WorldCat member libraries worldwide

The goal of this research monograph is to derive the analytic continuation and functional equation of the L-functions attached by R.P. Langlands to automorphic representations of reductive algebraic groups. The first part of the book (by Piatetski-Shapiro and Rallis) deals with L-functions for the simple classical groups; the second part (by Gelbart and Piatetski-Shapiro) deals with non-simple groups of the form G GL(n), with G a quasi-split reductive group of split rank n. The method of proof is to construct certain explicit zeta-integrals of Rankin-Selberg type which interpolate the relevant Langlands L-functions 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 and the oscillator representation by Stephen Rallis( Book )

16 editions published in 1987 in English and German and held by 360 WorldCat member libraries worldwide

These notes are concerned with showing the relation between L-functions 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 L-function (associated to the standard representation of the L-group 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 L-functions, (ii) see-saw dual reductive pairs and (iii) Siegel-Weil formula. The book addresses readers who specialize in the theory of automorphic forms and L-functions and the representation theory of Lie groups. N
L functions for the orthogonal group by D Ginzburg( Book )

13 editions published in 1997 in English and held by 231 WorldCat member libraries worldwide

Weil representation I : intertwining distributions and discrete spectrum by Stephen Rallis( Book )

17 editions published between 1974 and 1980 in English and German and held by 213 WorldCat member libraries worldwide

The descent map from automorphic representations of GL(n) to classical groups by D Ginzburg( Book )

13 editions published between 2010 and 2011 in English and Undetermined and held by 116 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 Gelfand-Graev type, or of Fourier-Jacobi 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
Automorphic representations, L-functions and applications : progress and prospects : proceedings of a conference honoring Steve Rallis on the occasion of his 60th birthday, the Ohio State University, March 27-30, 2003( Book )

1 edition published in 2005 in English and held by 78 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 3-4/2005
Méthodes mathématiques pour calculateurs arithmétiques by Anthony Ralston( Book )

1 edition published in 1965 in French and held by 19 WorldCat member libraries worldwide

Weil representation by Stephen Rallis( Book )

3 editions published in 1980 in Undetermined and English and held by 8 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

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

Intertwining distributions and discrete spectrum by Stephen Rallis( Book )

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

Représentations by Stephen Rallis( Book )

2 editions published between 1976 and 1979 in French and held by 3 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

L-functions and oscillator representation by Stephen Rallis( )

1 edition published in 1987 in English and held by 2 WorldCat member libraries worldwide

The Descent Map from Automorphic Representations of Gl(N) to Classical Groups by D Ginzburg( )

1 edition published in 2011 in English and held by 1 WorldCat member library worldwide

Annotation
On the Howe duality conjecture( )

1 edition published in 1984 in English and held by 1 WorldCat member library worldwide

Weil representation by Stephen Rallis( )

in Undetermined and held by 1 WorldCat member library worldwide

Feuilletages autonomes de r3. Branchements et enroulements, representations supercuspidales du groupe metaplectique, discrete spectrum of Weil representation by M Diener( Book )

1 edition published in 1977 in English and held by 0 WorldCat member libraries worldwide

 
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Explicit constructions of automorphic L-functions
Alternative Names
Rallis, S.

Rallis, S. 1942-

Rallis, Stephen 1942-...

Rallis, Steve 1942-...

Stephen James Rallis American mathematician

Languages
English (83)

French (4)

German (3)

Covers
L-functions and the oscillator representationL functions for the orthogonal groupThe descent map from automorphic representations of GL(n) to classical groupsAutomorphic representations, L-functions and applications : progress and prospects : proceedings of a conference honoring Steve Rallis on the occasion of his 60th birthday, the Ohio State University, March 27-30, 2003L-functions and oscillator representation