Advertisement

Congruences and Reduction mod p

  • Serge Lang
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 222)

Abstract

The study of modular forms modulo p was originated by Swinnerton-Dyer [Sw D], who determined the structure of the algebra of modular forms mod p. Serre then showed how one can extend this theory in many ways, and in particular obtained results concerning the congruence properties mod higher powers of p for the coefficients of the q-expansions of modular forms. After laying the basic foundations for the q-expansions, we reproduce Swinnerton-Dyer’s results, and then some of Serre’s basic results, referring to his more extensive papers for the continuation of the theory.

Keywords

Power Series Modular Form Preceding Theorem Integer Coefficient Power Series Ring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 1976

Authors and Affiliations

  • Serge Lang
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

Personalised recommendations