/

Automorphic Forms on SL2 (R)

Borel Armand
Heftet / 2008 / Engelsk

Produktdetaljer

ISBN
9780521072120
Publisert
2008-08-14
Utgiver
Vendor
Cambridge University Press
Vekt
310 gr
Høyde
229 mm
Bredde
152 mm
Dybde
12 mm
Aldersnivå
P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet
Antall sider
208

Forfatter
Borel Armand

Automorphic Forms on SL2 (R)

Borel Armand
Heftet / 2008 / Engelsk
Borel Armand
Heftet / 2008 / Engelsk
Nettpris:
721,-
Levering 7-20 dager
Sjekk lagerstatus i butikk

Review of the hardback: 'This text will serve as an admirable introduction to harmonic analysis as it appears in contemporary number theory and algebraic geometry.' Victor Snaith, Bulletin of the London Mathematical Society

Review of the hardback: '… carefully and concisely written … Clearly every mathematical library should have this book.' Zentralblatt

This book provides an introduction to some aspects of the analytic theory of automorphic forms on G=SL2(R) or the upper-half plane X, with respect to a discrete subgroup G of G of finite covolume. The point of view is inspired by the theory of infinite dimensional unitary representations of G; this is introduced in the last sections, making this connection explicit. The topics treated include the construction of fundamental domains, the notion of automorphic form on G\G and its relationship with the classical automorphic forms on X, Poincare series, constant terms, cusp forms, finite dimensionality of the space of automorphic forms of a given type, compactness of certain convolution operators, Eisenstein series, unitary representations of G, and the spectral decomposition of L2 (G\G). The main prerequisites are some results in functional analysis (reviewed, with references) and some familiarity with the elementary theory of Lie groups and Lie algebras. Graduate students and researchers in analytic number theory will find much to interest them in this book.
Les mer
Part I. Basic Material On SL2(R), Discrete Subgroups and the Upper-Half Plane: 1. Prerequisites and notation; 2. Review of SL2(R), differential operators, convolution; 3. Action of G on X, discrete subgroups of G, fundamental domains; 4. The unit disc model; Part II. Automorphic Forms and Cusp Forms: 5. Growth conditions, automorphic forms; 6. Poincare series; 7. Constant term:the fundamental estimate; 8. Finite dimensionality of the space of automorphic forms of a given type; 9. Convolution operators on cuspidal functions; Part III. Eisenstein Series: 10. Definition and convergence of Eisenstein series; 11. Analytic continuation of the Eisenstein series; 12. Eisenstein series and automorphic forms orthogonal to cusp forms; Part IV. Spectral Decomposition and Representations: 13.Spectral decomposition of L2(G\G)m with respect to C; 14. Generalities on representations of G; 15. Representations of SL2(R); 16. Spectral decomposition of L2(G\SL2(R)):the discrete spectrum; 17. Spectral decomposition of L2(G\SL2(R)): the continuous spectrum; 18. Concluding remarks.
Les mer
An introduction to the analytic theory of automorphic forms in the case of fuchsian groups.

Relaterte produkter

Review of the hardback: 'This text will serve as an admirable introduction to harmonic analysis as it appears in contemporary number theory and algebraic geometry.' Victor Snaith, Bulletin of the London Mathematical Society

Review of the hardback: '… carefully and concisely written … Clearly every mathematical library should have this book.' Zentralblatt

This book provides an introduction to some aspects of the analytic theory of automorphic forms on G=SL2(R) or the upper-half plane X, with respect to a discrete subgroup G of G of finite covolume. The point of view is inspired by the theory of infinite dimensional unitary representations of G; this is introduced in the last sections, making this connection explicit. The topics treated include the construction of fundamental domains, the notion of automorphic form on G\G and its relationship with the classical automorphic forms on X, Poincare series, constant terms, cusp forms, finite dimensionality of the space of automorphic forms of a given type, compactness of certain convolution operators, Eisenstein series, unitary representations of G, and the spectral decomposition of L2 (G\G). The main prerequisites are some results in functional analysis (reviewed, with references) and some familiarity with the elementary theory of Lie groups and Lie algebras. Graduate students and researchers in analytic number theory will find much to interest them in this book.
Les mer
Part I. Basic Material On SL2(R), Discrete Subgroups and the Upper-Half Plane: 1. Prerequisites and notation; 2. Review of SL2(R), differential operators, convolution; 3. Action of G on X, discrete subgroups of G, fundamental domains; 4. The unit disc model; Part II. Automorphic Forms and Cusp Forms: 5. Growth conditions, automorphic forms; 6. Poincare series; 7. Constant term:the fundamental estimate; 8. Finite dimensionality of the space of automorphic forms of a given type; 9. Convolution operators on cuspidal functions; Part III. Eisenstein Series: 10. Definition and convergence of Eisenstein series; 11. Analytic continuation of the Eisenstein series; 12. Eisenstein series and automorphic forms orthogonal to cusp forms; Part IV. Spectral Decomposition and Representations: 13.Spectral decomposition of L2(G\G)m with respect to C; 14. Generalities on representations of G; 15. Representations of SL2(R); 16. Spectral decomposition of L2(G\SL2(R)):the discrete spectrum; 17. Spectral decomposition of L2(G\SL2(R)): the continuous spectrum; 18. Concluding remarks.
Les mer
An introduction to the analytic theory of automorphic forms in the case of fuchsian groups.

Produktdetaljer

ISBN
9780521072120
Publisert
2008-08-14
Utgiver
Vendor
Cambridge University Press
Vekt
310 gr
Høyde
229 mm
Bredde
152 mm
Dybde
12 mm
Aldersnivå
P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet
Antall sider
208

Forfatter
Borel Armand

Relaterte produkter