Overview
- Provides an accessible introduction to the Arthur-Langlands conjectures, illustrated by numerous illuminating examples and concrete number theoretic applications
- Presents the arithmetic theory of automorphic forms for reductive groups over the integers, with an emphasis on phenomena not seen in the traditional GL(2) case
- Offers a self-contained approach to the theory of Euclidean lattices through the general theory of quadratic forms over Dedekind domains
Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (MATHE3, volume 69)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This book includes a self-contained approach of the general theory of quadratic forms and integral Euclidean lattices, as well as a presentation of the theory of automorphic forms and Langlands' conjectures, ranging from the first definitions to the recent and deep classification results due to James Arthur.
Its connecting thread is a question about lattices of rank 24: the problem of p-neighborhoods between Niemeier lattices. This question, whose expression is quite elementary, is in fact very natural from the automorphic point of view, and turns out to be surprisingly intriguing. We explain how the new advances in the Langlands program mentioned above pave the way for a solution. This study proves to be very rich, leading us to classical themes such as theta series, Siegel modular forms, the triality principle, L-functions and congruences between Galois representations.
This monograph is intended for any mathematician with an interest in Euclidean lattices, automorphic forms or number theory. A large part of it is meant to be accessible to non-specialists.
Authors and Affiliations
About the authors
Jean Lannes is a topologist and Emeritus Professor at Université Paris Diderot.
Bibliographic Information
Book Title: Automorphic Forms and Even Unimodular Lattices
Book Subtitle: Kneser Neighbors of Niemeier Lattices
Authors: Gaëtan Chenevier, Jean Lannes
Translated by: Reinie Erné
Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
DOI: https://doi.org/10.1007/978-3-319-95891-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-319-95890-3Published: 15 March 2019
eBook ISBN: 978-3-319-95891-0Published: 28 February 2019
Series ISSN: 0071-1136
Series E-ISSN: 2197-5655
Edition Number: 1
Number of Pages: XXI, 417
Number of Illustrations: 23 b/w illustrations, 1 illustrations in colour
Topics: Number Theory, Algebra, Discrete Mathematics