Modular Functions Of One Variable Iii: Proceedings International Summer School, University Of Antwerp, Ruca, July 17 - August 3, 1972 (lecture Notes In Mathematics)

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-Æ. 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 Content: Front Matter....Pages I-V On l-ADIC Representations and Congruences for Coefficients of Modular Forms....Pages 1-55 The Up operator of Atkin on modular functions of level 2 with growth conditions....Pages 57-67 P-ADIC Properties of Modular Schemes and Modular Forms....Pages 69-190 Formes modulaires et fonctions zêta p-adiques....Pages 191-268 Certains calculs numériques relatifs � l’interpolation p-adique des séries de Dirichlet....Pages 269-349 Back Matter....Pages 350-350 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. 2 Volume 3 is devoted to p-adic properties of modular forms and applications to l-adic representations and zeta functions. of Belgium, Rank Xerox Belgium, the Fort Food Co.