Contributions in Mathematical and Computational Sciences

Computations with Modular Forms

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

Editors: Böckle, Gebhard, Wiese, Gabor (Eds.)

  • 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
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  • Due: October 7, 2016
  • ISBN 978-3-319-35479-8
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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.

Table of contents (14 chapters)

  • Lectures on Computing Cohomology of Arithmetic Groups

    Gunnells, Paul E.

    Pages 3-45

  • Computing with Algebraic Automorphic Forms

    Loeffler, David

    Pages 47-68

  • Overconvergent Modular Symbols

    Pollack, Robert

    Pages 69-105

  • Congruence Subgroups, Cusps and Manin Symbols over Number Fields

    Cremona, J. E. (et al.)

    Pages 109-127

  • Computing Weight One Modular Forms over $\mathbb{C}$ and $\overline{\mathbb{F}}_{p}$

    Buzzard, Kevin

    Pages 129-146

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-319-03847-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-319-03846-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: October 7, 2016
  • ISBN 978-3-319-35479-8
  • Free shipping for individuals worldwide
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Computations with Modular Forms
Book Subtitle
Proceedings of a Summer School and Conference, Heidelberg, August/September 2011
Editors
  • Gebhard Böckle
  • Gabor Wiese
Series Title
Contributions in Mathematical and Computational Sciences
Series Volume
6
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-03847-6
DOI
10.1007/978-3-319-03847-6
Hardcover ISBN
978-3-319-03846-9
Softcover ISBN
978-3-319-35479-8
Series ISSN
2191-303X
Edition Number
1
Number of Pages
XII, 376
Number of Illustrations and Tables
17 b/w illustrations, 12 illustrations in colour
Topics