Gelbart, Stephen S. 1946
Overview
Works:  48 works in 250 publications in 4 languages and 4,294 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Honoree, Dedicatee 
Classifications:  QA3, 512.22 
Publication Timeline
.
Most widely held works by
Stephen S Gelbart
Lectures on analysis by
Gustave Choquet(
Book
)
8 editions published between 1969 and 1976 in English and held by 525 WorldCat member libraries worldwide
8 editions published between 1969 and 1976 in English and held by 525 WorldCat member libraries worldwide
Automorphic forms on Adele groups by
Stephen S Gelbart(
Book
)
17 editions published between 1975 and 2016 in English and Undetermined and held by 451 WorldCat member libraries worldwide
This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups. Interpreting important recent contributions of Jacquet and Langlands, the author presents new and previously inaccessible results, and systematically develops explicit consequences and connections with the classical theory. The underlying theme is the decomposition of the regular representation of the adele group of GL(2). A detailed proof of the celebrated trace formula of Selberg is included, with a discussion of the possible range of applicability of this formula. Throughout the work the author emphasizes new examples and problems that remain open within the general theory. TABLE OF CONTENTS: 1. The Classical Theory 2. Automorphic Forms and the Decomposition of L2(PSL(2,R) 3. Automorphic Forms as Functions on the Adele Group of GL(2) 4. The Representations of GL(2) over Local and Global Fields 5. Cusp Forms and Representations of the Adele Group of GL(2) 6. Hecke Theory for GL(2) 7. The Construction of a Special Class of Automorphic Forms 8. Eisenstein Series and the Continuous Spectrum 9. The Trace Formula for GL(2) 10. Automorphic Forms on a Quaternion Algebra
17 editions published between 1975 and 2016 in English and Undetermined and held by 451 WorldCat member libraries worldwide
This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups. Interpreting important recent contributions of Jacquet and Langlands, the author presents new and previously inaccessible results, and systematically develops explicit consequences and connections with the classical theory. The underlying theme is the decomposition of the regular representation of the adele group of GL(2). A detailed proof of the celebrated trace formula of Selberg is included, with a discussion of the possible range of applicability of this formula. Throughout the work the author emphasizes new examples and problems that remain open within the general theory. TABLE OF CONTENTS: 1. The Classical Theory 2. Automorphic Forms and the Decomposition of L2(PSL(2,R) 3. Automorphic Forms as Functions on the Adele Group of GL(2) 4. The Representations of GL(2) over Local and Global Fields 5. Cusp Forms and Representations of the Adele Group of GL(2) 6. Hecke Theory for GL(2) 7. The Construction of a Special Class of Automorphic Forms 8. Eisenstein Series and the Continuous Spectrum 9. The Trace Formula for GL(2) 10. Automorphic Forms on a Quaternion Algebra
Weil's representation and the spectrum of the metaplectic group by
Stephen S Gelbart(
Book
)
22 editions published between 1976 and 2008 in 3 languages and held by 393 WorldCat member libraries worldwide
22 editions published between 1976 and 2008 in 3 languages and held by 393 WorldCat member libraries worldwide
Explicit constructions of automorphic Lfunctions by
Stephen S Gelbart(
Book
)
17 editions published in 1987 in 3 languages and held by 356 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
17 editions published in 1987 in 3 languages and held by 356 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
An introduction to the Langlands program by
Daniel Bump(
Book
)
13 editions published between 2003 and 2004 in English and held by 329 WorldCat member libraries worldwide
For the past several decades the theory of automorphic forms has become a major focal point of development in number theory and algebraic geometry, with applications in many diverse areas, including combinatorics and mathematical physics. The twelve chapters of this monograph present a broad, userfriendly introduction to the Langlands program, that is, the theory of automorphic forms and its connection with the theory of Lfunctions and other fields of mathematics. Key features of this selfcontained presentation: A variety of areas in number theory from the classical zeta function up to the Langlands program are covered. The exposition is systematic, with each chapter focusing on a particular topic devoted to special cases of the program: Basic zeta function of Riemann and its generalizations to Dirichlet and Hecke Lfunctions, class field theory and some topics on classical automorphic functions (E. Kowalski) A study of the conjectures of Artin and ShimuraTaniyamaWeil (E. de Shalit) An examination of classical modular (automorphic) Lfunctions as GL(2) functions, bringing into play the theory of representations (S.S. Kudla) Selberg's theory of the trace formula, which is a way to study automorphic representations (D. Bump) Discussion of cuspidal automorphic representations of GL(2, (A)) leads to Langlands theory for GL(n) and the importance of the Langlands dual group (J.W. Cogdell) An introduction to the geometric Langlands program, a new and active area of research that permits using powerful methods of algebraic geometry to construct automorphic sheaves (D. Gaitsgory) Graduate students and researchers will benefit from this beautiful text
13 editions published between 2003 and 2004 in English and held by 329 WorldCat member libraries worldwide
For the past several decades the theory of automorphic forms has become a major focal point of development in number theory and algebraic geometry, with applications in many diverse areas, including combinatorics and mathematical physics. The twelve chapters of this monograph present a broad, userfriendly introduction to the Langlands program, that is, the theory of automorphic forms and its connection with the theory of Lfunctions and other fields of mathematics. Key features of this selfcontained presentation: A variety of areas in number theory from the classical zeta function up to the Langlands program are covered. The exposition is systematic, with each chapter focusing on a particular topic devoted to special cases of the program: Basic zeta function of Riemann and its generalizations to Dirichlet and Hecke Lfunctions, class field theory and some topics on classical automorphic functions (E. Kowalski) A study of the conjectures of Artin and ShimuraTaniyamaWeil (E. de Shalit) An examination of classical modular (automorphic) Lfunctions as GL(2) functions, bringing into play the theory of representations (S.S. Kudla) Selberg's theory of the trace formula, which is a way to study automorphic representations (D. Bump) Discussion of cuspidal automorphic representations of GL(2, (A)) leads to Langlands theory for GL(n) and the importance of the Langlands dual group (J.W. Cogdell) An introduction to the geometric Langlands program, a new and active area of research that permits using powerful methods of algebraic geometry to construct automorphic sheaves (D. Gaitsgory) Graduate students and researchers will benefit from this beautiful text
Analytic properties of automorphic Lfunctions by
Stephen S Gelbart(
Book
)
13 editions published in 1988 in English and Undetermined and held by 242 WorldCat member libraries worldwide
13 editions published in 1988 in English and Undetermined and held by 242 WorldCat member libraries worldwide
Lectures on the ArthurSelberg trace formula by
Stephen S Gelbart(
Book
)
12 editions published in 1996 in English and held by 232 WorldCat member libraries worldwide
12 editions published in 1996 in English and held by 232 WorldCat member libraries worldwide
Fourier analysis on matrix space by
Stephen S Gelbart(
Book
)
18 editions published between 1971 and 1977 in 3 languages and held by 217 WorldCat member libraries worldwide
18 editions published between 1971 and 1977 in 3 languages and held by 217 WorldCat member libraries worldwide
Automorphic forms and Lfunctions : a workshop in honor of Steve Gelbart on the occasion of his sixtieth birthday, May 1519,
2006, Rehovot and TelAviv, Israel by Workshop on Automorphic Forms and LFunctions(
Book
)
22 editions published between 2006 and 2009 in English and held by 176 WorldCat member libraries worldwide
22 editions published between 2006 and 2009 in English and held by 176 WorldCat member libraries worldwide
Automorphic forms, representation theory and arithmetic : papers presented at the Bombay Colloquium 1979 by
Stephen S Gelbart(
Book
)
17 editions published in 1981 in 3 languages and held by 174 WorldCat member libraries worldwide
17 editions published in 1981 in 3 languages and held by 174 WorldCat member libraries worldwide
Festschrift in honor of I.I. PiatetskiShapiro on the occasion of his sixtieth birthday(
Book
)
4 editions published in 1990 in English and held by 77 WorldCat member libraries worldwide
4 editions published in 1990 in English and held by 77 WorldCat member libraries worldwide
Lectures on analysis. Représentation theory by
Gustave Choquet(
Book
)
7 editions published between 1969 and 1976 in English and held by 64 WorldCat member libraries worldwide
7 editions published between 1969 and 1976 in English and held by 64 WorldCat member libraries worldwide
Lectures on analysis. Infinite dimensional measures and problem solutions by
Gustave Choquet(
Book
)
8 editions published between 1969 and 1976 in English and Spanish and held by 58 WorldCat member libraries worldwide
8 editions published between 1969 and 1976 in English and Spanish and held by 58 WorldCat member libraries worldwide
Lectures on analysis. Integration and topological vector spaces by
Gustave Choquet(
Book
)
8 editions published between 1969 and 1976 in English and held by 54 WorldCat member libraries worldwide
8 editions published between 1969 and 1976 in English and held by 54 WorldCat member libraries worldwide
The Schur lectures (1992) by
Roger Howe(
Book
)
5 editions published in 1995 in English and held by 46 WorldCat member libraries worldwide
5 editions published in 1995 in English and held by 46 WorldCat member libraries worldwide
The Schur lectures (1992) : Roger Howe, Perspectives on invariant theory : Peter Sarnak, Arithmetic quantum chaos(
Book
)
3 editions published in 1995 in English and held by 36 WorldCat member libraries worldwide
3 editions published in 1995 in English and held by 36 WorldCat member libraries worldwide
Explicit Constructions of Automorphic LFunctions by
Stephen S Gelbart(
)
1 edition published in 1987 in English and held by 29 WorldCat member libraries worldwide
1 edition published in 1987 in English and held by 29 WorldCat member libraries worldwide
Automorphic forms and representations of Adele groups by
Stephen S Gelbart(
Book
)
5 editions published in 1975 in English and held by 19 WorldCat member libraries worldwide
5 editions published in 1975 in English and held by 19 WorldCat member libraries worldwide
Encyclopaedia of mathematics. Supplement III by
Shreeram Shankar Abhyankar(
)
1 edition published in 2002 in English and held by 0 WorldCat member libraries worldwide
This is the third supplementary volume to Kluwer's highly acclaimed twelvevolume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and uptodate Encyclopaedia of Mathematics available
1 edition published in 2002 in English and held by 0 WorldCat member libraries worldwide
This is the third supplementary volume to Kluwer's highly acclaimed twelvevolume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and uptodate Encyclopaedia of Mathematics available
Analytic Properties of Automorphic LFunctions by
Stephen S Gelbart(
)
1 edition published in 2014 in English and held by 0 WorldCat member libraries worldwide
Analytic Properties of Automorphic LFunctions
1 edition published in 2014 in English and held by 0 WorldCat member libraries worldwide
Analytic Properties of Automorphic LFunctions
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Related Identities
 Lance, T. (Tim) Editor
 Choquet, Gustave Author
 Marsden, Jerrold E. Author Editor
 Pi︠a︡tet︠s︡kiĭShapiro, I. I. (Ilʹi︠a︡ Iosifovich) 19292009 Honoree Author Editor
 Rallis, Stephen 1942 Author
 Bernstein, Joseph 1945 Editor
 Bump, Daniel 1952 Author Editor
 Shahidi, Freydoon
 Ginzburg, D. (David) Editor
 Lapid, Erez 1971 Editor
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Associated Subjects
Adeles Algebra Arithmetic Automorphic forms Automorphic functions Calculus Canada Complex manifolds Fourier series Fourier transformations Functions, Zeta Geometry, Algebraic Global analysis (Mathematics) Group actions (Mathematics) Hamiltonian systems Harmonic analysis Integration, Functional Invariants Lfunctions Lie groups Linear algebraic groups Linear topological spaces Mathematical analysis Mathematics Matrices Measure theory Number theory Pi︠a︡tet︠s︡kiĭShapiro, I. I.(Ilʹi︠a︡ Iosifovich), Quantum chaos Representations of groups Scientists Selberg trace formula Topological groups United States
Alternative Names
Gelbart, S.
Gelbart, S. 1946
Gelbart, S. S. 1946
Gelbart, S. (Stephen), 1946
Gelbarṭ, Sṭepan 1946...
Gelbart, Stephen.
Gelbart, Stephen 1946
Gelbart, Stephen S.
Gelbart, Stephen S. 1946
Gelbart, Stephen Samuel 1946
Gelbart, Steve 1946
Stephen Gelbart American mathematician
Stephen Gelbart Amerikaans wiskundige
Stephen Gelbart israelischUSamerikanischer Mathematiker
גלברט סטפן 1946....
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