Introduction to Modular Forms

1. Auflage 1976. Corr. 3rd printing. Softcover version of original hardcover Auflage 1987
ISBN: 978-3-642-05716-8
Verlag: Springer

Buch, Englisch, Band 222, 265 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 423 g

Reihe: Grundlehren der mathematischen Wissenschaften

From the reviews: "This book gives a thorough introduction to several theories that are fundamental to research on modular forms. Most of the material, despite its importance, had previously been unavailable in textbook form. Complete and readable proofs are given... In conclusion, this book is a welcome addition to the literature for the growing number of students and mathematicians in other fields who want to understand the recent developments in the theory of modular forms."
#Mathematical Reviews#
"This book will certainly be indispensable to all those wishing to get an up-to-date initiation to the theory of modular forms."
#Publicationes Mathematicae#

Zielgruppe

Research

Autoren/Hrsg.

Lang, Serge

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

I. Classical Theory.- I. Modular Forms.- II. Hecke Operators.- III. Petersson Scalar Product.- Appendix by D. Zagier. The Eichler-Selberg Trace Formula on SL2(Z).- II. Periods of Cusp Forms.- IV. Modular Symbols.- V. Coefficients and Periods of Cusp Forms on SL2(Z).- VI. The Eichler-Shimura Isomorphism on SL2(Z).- III. Modular Forms for Congruence Subgroups.- VII. Higher Levels.- VIII. Atkin-Lehner Theory.- IX. The Dedekind Formalism.- IV. Congruence Properties and Galois Representations.- X. Congruences and Reduction mod p.- XI. Galois Representations.- V. p-Adic Distributions.- XII. General Distributions.- XIII. Bernoulli Numbers and Polynomials.- XIV. The Complex L-Functions.- XV. The Hecke-Eisenstein and Klein Forms.