Modular functions of one variable : proceedings, International Summer School, University of Antwerp, RUCA, July 17-August 3, 1972

Author(s)

• International Summer School on Modular Functions
• Kuyk, Willem
• Deligne, Pierre
• Serre, Jean Pierre
• Birch, Bryan John

Bibliographic Information

Modular functions of one variable : proceedings, International Summer School, University of Antwerp, RUCA, July 17-August 3, 1972

edited by Willem Kuyk

（Lecture notes in mathematics, 320, 349, 350, 476）

Springer-Verlag, 1973-1975

• v. 1 : gw
• v. 1 : us
• v. 2 : gw
• v. 2 : us
• v. 3 : gw
• v. 3 : us
• v. 4 : gw
• v. 4 : us

Note

A NATO Advanced Study Institute

Vol. 2 edited by P. Deligne and W. Kuyk; v. 3 by W. Kuyk and J.-P. Serre; v. 4 by B.J. Birch and W. Kuyk

Includes bibliographies

Description and Table of Contents

Volume

v. 1 : gw ISBN 9783540062196

Description

An international Summer School on: "Modular functions of one variable and arithmetical applications" took place at RUCA, Antwerp University, from July 17 to - gust 3, 1972. This book is the first volume (in a series of four) of the Proceedings of the Summer School. It includes the basic course given by A. Ogg, and several other papers with a strong analyt~c flavour. Volume 2 contains the courses of R. P. Langlands (l-adic rep resentations) and P. Deligne (modular schemes - representations of GL ) and papers on related topics. 2 Volume 3 is devoted to p-adic properties of modular forms and applications to l-adic representations and zeta functions. Volume 4 collects various material on elliptic curves, includ ing numerical tables. The School was a NATO Advanced Study Institute, and the orga nizers want to thank NATO for its major subvention. Further support, in various forms, was received from IBM Belgium, the Coca-Cola Co. of Belgium, Rank Xerox Belgium, the Fort Food Co. of Belgium, and NSF Washington, D.C** We extend our warm est thanks to all of them, as well as to RUCA and the local staff (not forgetting hostesses and secretaries!) who did such an excellent job.

Table of Contents

Survey of Modular Functions of One Variable.- Complex Multiplication.- Modular Forms of Half Integral Weight.- The Basis Problem for Modular Forms and the Traces of the Hecke Operators.- Class-Numbers of Complex Quadratic Fields.- Some Calculations of Modular Relations.- On the Aq (?) ? Bq (?) Conjecture.

Volume

v. 3 : gw ISBN 9783540064831

Description

This is Volume 3 of the Proceedings of the Interna- tional Summer School on "Modular functions of one variable and arithmetical applications" which took place at RUCA, Antwerp University, from July 17 to August 3, 1972. It contains papers by P.Cartier-[yen].Roy, B.Dwork, N.Katz, J-P.Serre and H.P.F.Swinnerton-Dyer on congruence proper- ties of modular forms, l-adic representations, p-adic modular forms and p-adic zeta functions. W.Kuyk J-P.Serre CONTENTS H.P.F. SWINNERTON-DYER On l-adic representations and congruences for coefficients 1 of modular forms B. DWORK The Up operator of Atkin on modular functions of level 2 57 with growth conditions N. KATZ p-adic properties of modular 69 schemes and modular forms J-P. SERRE Formes modulaires et fonctions 191 zeta p-adiques P. CARTIER-Y. ROY Certains calculs numeriques relatifs a l'interpolation 269 p-adique des series de Dirichlet Mailing addresses of authors 350 He~~n e.L. Siegel gewidmet ON l-ADIC REPRESENTATIONS AND CONGRUENCES FOR COEFFICIENTS OF MODULAR FORMS BY H.P.F. SWINNERTON-DYER International Summer School on Modular Functions Antwerp 1972 2 SwD-2 CONTENTS 1. Introduction. p.3 2. The possible images of Pl. p.l0 3. Modular forms mod l. p.1S 4. The exceptional primes. p.26 5. Congruences modulo powers of l. p.36 Appendix p.43 References p.ss 3 SwD-3 ON l-ADIC REPRESENTATIONS AND CONGRUENCES FOR COEFFICIENTS OF MODULAR FORMS * 1. Introduction.

Table of Contents

On ?-ADIC Representations and Congruences for Coefficients of Modular Forms.- The Up operator of Atkin on modular functions of level 2 with growth conditions.- P-ADIC Properties of Modular Schemes and Modular Forms.- Formes modulaires et fonctions zeta p-adiques.- Certains calculs numeriques relatifs a l'interpolation p-adique des series de Dirichlet.

Volume

v. 2 : gw ISBN 9783540065586

Description

This is Volume 2 of the Proceedings of the International Summer School on "Modular functions of one variable and arithmetical applications" which took place at RUCA, Antwerp University, from July 17 till August 3, 1972. It contains papers by W. Casselman, P. Deligne, R. Langlands and 1. 1. Piateckii-Shapiro. Its theme is the interplay between modular schemes for elliptic curves, and representations of GL(2). P. Deligne W. Kuyk CONTENTS W. CASSELMAN An assortment of results on represen- 1 tations of GL (k) 2 P. DELIGNE Formes mOdulaires et representations 55 de GL(2) W. CASSELMAN On representations of GL and the arith- 107 2 metic of modular curves P. DELIGNE - M. RAPOPORT Les schemas de modules de courbes ellip- 143 tiques 1. 1. PIATECKII-SHAPIRO Zeta-functions of modular curves 317 R. P. LANGLANDS Modular forms and t-adic representations 361 P. DELIGNE Les constantes des equations fonctionnelles 501 des fonctions L Addresses of authors 598 AN ASSORTMENT OF RESULTS ON REPRESENTATIONS OF GL (k) 2 by W. Casselman~ International Summer School on Modular Functions} Antwerp 1972 ~ The author's travel expences for this conference were paid for by a grant from the National Research Council of Canada. -2- Cas-2 Contents Introduction 3 Notations 1. Generalities 5 Appendix 2. The principal series representations of 15 GL (O) and the associated Hecke algebras 2 3. The principal series of G 29 4.

Table of Contents

An Assortment of Results on Representations of GL2(k).- Formes Modulaires et Representations De GL(2).- On Representations of Gl2 and The Arithmetic of Modular Curves.- Les Schemas de Modules de Courbes Elliptiques.- Zeta-Functions of Modular Curves.- Modular Forms and ?-Adic Representations.- Les Constantes des Equations Fonctionnelles des Fonctions L.

Volume

v. 4 : gw ISBN 9783540073925

Table of Contents

Ellitpic curves and modular functions.- Algorithm for determining the type of a singular fiber in an elliptic pencil.- Courbes elliptiques: Formulaire.- Sources and reliability of the tables.- Remarks on isogenies.- Table 1.- Table 2.- Table 3.- Table 4.- Table 5.- Table 6.

by "Nielsen BookData"

Details

• NCID: BA06734543
• ISBN:
  • 354006219X
  • 038706219X
  • 354006558X
  • 038706558X
  • 3540064834
  • 0387064834
  • 3540073922
  • 0387073922
• LCCN: 73078427
• Country Code: gw
• Title Language Code: eng
• Text Language Code: engfre
• Place of Publication: Berlin ; New York
• Pages/Volumes: 4 v.
• Size: 25 - 28 cm
• Classification:
  • LCC : QA3
  • LCC : QA343
  • DC : 510/.8 s
  • DC : 515/.9
• Subject Headings:
  • LCSH : Functions, Modular -- Congresses
• Parent Bibliography ID:
  • BA00146586