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Serre's A Course in Arithmetic is a concentrated, modern introduction to basically three areas of number theory, quadratic forms, Dirichlet's density theorem, and modular forms. The first edition was very well accepted and is now one of the leading introductory texts on the advanced undergraduate or beginning graduate level.From the reviews: "... The book is carefully written - in particular very much self-contained. As was the intention of the author, it is easily accessible to graduate or even undergraduate students, yet even the advanced mathematician will enjoy reading it. The last chapter, more difficult for the beginner, is an introduction to contemporary problems." American Scientist
This volume is the offspring of a week-long workshop on "Galois
groups over Q and related topics," which was held at the
Mathematical Sciences Research Institute during the week March
23-27, 1987. The organizing committee consisted of Kenneth Ribet
(chairman), Yasutaka Ihara, and Jean-Pierre Serre. The conference
focused on three principal themes: 1. Extensions of Q with finite
simple Galois groups. 2. Galois actions on fundamental groups,
nilpotent extensions of Q arising from Fermat curves, and the
interplay between Gauss sums and cyclotomic units. 3.
Representations of Gal(Q/Q) with values in GL(2)j deformations and
connections with modular forms. Here is a summary of the conference
program: * G. Anderson: "Gauss sums, circular units and the
simplex" * G. Anderson and Y. Ihara: "Galois actions on 11"1 ( ***
) and higher circular units" * D. Blasius: "Maass forms and Galois
representations" * P. Deligne: "Galois action on 1I"1(P-{0, 1, oo})
and Hodge analogue" * W. Feit: "Some Galois groups over number
fields" * Y. Ihara: "Arithmetic aspect of Galois actions on 1I"1(P
- {O, 1, oo})" - survey talk * U. Jannsen: "Galois cohomology of
i-adic representations" * B. Matzat: - "Rationality criteria for
Galois extensions" - "How to construct polynomials with Galois
group Mll over Q" * B. Mazur: "Deforming GL(2) Galois
representations" * K. Ribet: "Lowering the level of modular
representations of Gal( Q/ Q)" * J-P. Serre: - Introductory Lecture
- "Degree 2 modular representations of Gal(Q/Q)" * J.
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.
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Modular Functions of One Variable VI, No. VI - Proceedings International Conference, University of Bonn, Sonderforschungsbereich Theoretische Mathematik, July 2-14, 1976 (English, French, Paperback, 1977 ed.)
J.P. Serre, D. B. Zagier
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