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Arithmetic of p-adic Modular Forms

  • Authors
  • Fernando Quadros Gouvêa

Part of the Lecture Notes in Mathematics book series (LNM, volume 1304)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Fernando Quadros Gouvêa
    Pages 1-29
  3. Fernando Quadros Gouvêa
    Pages 30-70
  4. Fernando Quadros Gouvêa
    Pages 71-116
  5. Back Matter
    Pages 117-121

About this book

Introduction

The central topic of this research monograph is the relation between p-adic modular forms and p-adic Galois representations, and in particular the theory of deformations of Galois representations recently introduced by Mazur. The classical theory of modular forms is assumed known to the reader, but the p-adic theory is reviewed in detail, with ample intuitive and heuristic discussion, so that the book will serve as a convenient point of entry to research in that area. The results on the U operator and on Galois representations are new, and will be of interest even to the experts. A list of further problems in the field is included to guide the beginner in his research. The book will thus be of interest to number theorists who wish to learn about p-adic modular forms, leading them rapidly to interesting research, and also to the specialists in the subject.

Keywords

Area arithmetic boundary element method duality field form function functions modular form operator presentation review theorem

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0082111
  • Copyright Information Springer-Verlag Berlin Heidelberg 1988
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-18946-6
  • Online ISBN 978-3-540-38854-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site