Computations with Modular Forms

Proceedings of a Summer School and Conference, Heidelberg, August/September 2011

  • Gebhard Böckle
  • Gabor Wiese
Conference proceedings

DOI: 10.1007/978-3-319-03847-6

Part of the Contributions in Mathematical and Computational Sciences book series (CMCS, volume 6)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Summer School

    1. Front Matter
      Pages 1-1
    2. David Loeffler
      Pages 47-68
    3. Robert Pollack
      Pages 69-105
  3. Conference and Research Contributions

About these proceedings

Introduction

This volume contains original research articles, survey articles and lecture notes related to the Computations with Modular Forms 2011 Summer School and Conference, held at the University of Heidelberg. A key theme of the Conference and Summer School was the interplay between theory, algorithms and experiment.

The 14 papers offer readers both, instructional courses on the latest algorithms for computing modular and automorphic forms, as well as original research articles reporting on the latest developments in the field.

The three Summer School lectures provide an introduction to modern algorithms together with some theoretical background for computations of and with modular forms, including computing cohomology of arithmetic groups, algebraic automorphic forms, and overconvergent modular symbols.

The 11 Conference papers cover a wide range of themes related to computations with modular forms, including lattice methods for algebraic modular forms on classical groups, a generalization of the Maeda conjecture, an efficient algorithm for special values of p-adic Rankin triple product L-functions, arithmetic aspects and experimental data of Bianchi groups, a theoretical study of the real Jacobian of modular curves, results on computing weight one modular forms, and more.

Keywords

algorithms cohomology of arithmetic groups computations in number theory computations of cohomology groups modular and automorphic forms

Editors and affiliations

  • Gebhard Böckle
    • 1
  • Gabor Wiese
    • 2
  1. 1.Interdisciplinary Center for Scientific ComputingUniversität HeidelbergHeidelbergGermany
  2. 2.UR MathématiquesFaculté des Sciences, de la Technologie et de la CommunicationLuxembourgLuxembourg

Bibliographic information

  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-03846-9
  • Online ISBN 978-3-319-03847-6
  • Series Print ISSN 2191-303X
  • Series Online ISSN 2191-3048