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  • Conference proceedings
  • © 2014

Computations with Modular Forms

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

  • Unites lecture notes and research articles; lecture notes prepare the reader for most research articles

  • Covers latest developments in algorithmic aspects of modular forms

  • Targeted at graduate students and researchers in algorithmic number theory and modular forms

  • Includes supplementary material: sn.pub/extras

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

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eBook USD 189.00
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  • ISBN: 978-3-319-03847-6
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Hardcover Book USD 249.99
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Table of contents (14 papers)

  1. Front Matter

    Pages I-XII
  2. Summer School

    1. Front Matter

      Pages 1-1
    2. Computing with Algebraic Automorphic Forms

      • David Loeffler
      Pages 47-68
    3. Overconvergent Modular Symbols

      • Robert Pollack
      Pages 69-105

About this book

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

  • Interdisciplinary Center for Scientific Computing, Universität Heidelberg, Heidelberg, Germany

    Gebhard Böckle

  • UR Mathématiques, Faculté des Sciences, de la Technologie et de la Communication, Luxembourg, Luxembourg

    Gabor Wiese

Bibliographic Information

Buying options

eBook USD 189.00
Price excludes VAT (USA)
  • ISBN: 978-3-319-03847-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book USD 249.99
Price excludes VAT (USA)