Authors:
- Offers a comprehensive and solid introduction to the theory
- Includes exercises and solutions
- Presents a unique collection of knowledge on this theory not available elsewhere
Part of the book series: Pathways in Mathematics (PATHMATH)
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Table of contents (10 chapters)
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Front Matter
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The ‘Eigen’ Construction
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Front Matter
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Modular Symbols and L-Functions
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Front Matter
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The Eigencurve and its p-Adic L-Functions
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Front Matter
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Back Matter
About this book
This book discusses the p-adic modular forms, the eigencurve that parameterize them, and the p-adic L-functions one can associate to them. These theories and their generalizations to automorphic forms for group of higher ranks are of fundamental importance in number theory.
For graduate students and newcomers to this field, the book provides a solid introduction to this highly active area of research. For experts, it will offer the convenience of collecting into one place foundational definitions and theorems with complete and self-contained proofs.
Written in an engaging and educational style, the book also includes exercises and provides their solution.
Reviews
“Complete proofs (or detailed references) of all statements are given and many exercises (with their solutions or hints) are included, hence the book may be addressed to graduate students working in this beautiful area of number theory and arithmetic algebraic geometry. This is a welcome addition to the literature in a field.” (Andrzej Dąbrowski, zbMATH 1493.11002, 2022)
Authors and Affiliations
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Department of Mathematics, Brandeis University, Waltham, USA
Joël Bellaïche
About the author
Bibliographic Information
Book Title: The Eigenbook
Book Subtitle: Eigenvarieties, families of Galois representations, p-adic L-functions
Authors: Joël Bellaïche
Series Title: Pathways in Mathematics
DOI: https://doi.org/10.1007/978-3-030-77263-5
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-77262-8Published: 13 August 2021
Softcover ISBN: 978-3-030-77265-9Published: 14 August 2022
eBook ISBN: 978-3-030-77263-5Published: 11 August 2021
Series ISSN: 2367-3451
Series E-ISSN: 2367-346X
Edition Number: 1
Number of Pages: XI, 316
Number of Illustrations: 15 b/w illustrations, 1 illustrations in colour
Topics: Number Theory