Computations with Modular Forms
Proceedings of a Summer School and Conference, Heidelberg, August/September 2011
Editors: Böckle, Gebhard, Wiese, Gabor (Eds.)
Free Preview- 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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- About this book
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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)
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Lectures on Computing Cohomology of Arithmetic Groups
Pages 3-45
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Computing with Algebraic Automorphic Forms
Pages 47-68
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Overconvergent Modular Symbols
Pages 69-105
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Congruence Subgroups, Cusps and Manin Symbols over Number Fields
Pages 109-127
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Computing Weight One Modular Forms over $\mathbb{C}$ and $\overline{\mathbb{F}}_{p}$
Pages 129-146
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Table of contents (14 chapters)
- Download Preface 1 PDF (89.7 KB)
- Download Sample pages 1 PDF (996.5 KB)
- Download Table of contents PDF (76 KB)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Computations with Modular Forms
- Book Subtitle
- Proceedings of a Summer School and Conference, Heidelberg, August/September 2011
- Editors
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- 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
- 17 b/w illustrations, 12 illustrations in colour
- Topics
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