Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics

Automorphic Forms and Even Unimodular Lattices

Kneser Neighbors of Niemeier Lattices

Authors: Chenevier, Gaëtan, Lannes, Jean

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  • ​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
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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.

About the authors

Gaëtan Chenevier is a number theorist and Senior CNRS Researcher at Université Paris-Sud.
Jean Lannes is a topologist and Emeritus Professor at Université Paris Diderot.

Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook 85,59 €
price for Spain (gross)
  • ISBN 978-3-319-95891-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • Immediate eBook download after purchase and usable on all devices
  • Bulk discounts from 10 eBooks
Hardcover 103,99 €
price for Spain (gross)
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Bibliographic Information

Bibliographic Information
Book Title
Automorphic Forms and Even Unimodular Lattices
Book Subtitle
Kneser Neighbors of Niemeier Lattices
Authors
Translated by
Erné, R.
Series Title
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Series Volume
69
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-319-95891-0
DOI
10.1007/978-3-319-95891-0
Hardcover ISBN
978-3-319-95890-3
Series ISSN
0071-1136
Edition Number
1
Number of Pages
XXI, 417
Number of Illustrations
23 b/w illustrations, 1 illustrations in colour
Topics