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Automorphic Forms and Even Unimodular Lattices

Kneser Neighbors of Niemeier Lattices

  • Gaëtan Chenevier
  • Jean Lannes

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Gaëtan Chenevier, Jean Lannes
    Pages 1-17
  3. Gaëtan Chenevier, Jean Lannes
    Pages 19-43
  4. Gaëtan Chenevier, Jean Lannes
    Pages 45-87
  5. Gaëtan Chenevier, Jean Lannes
    Pages 89-122
  6. Gaëtan Chenevier, Jean Lannes
    Pages 123-144
  7. Gaëtan Chenevier, Jean Lannes
    Pages 145-175
  8. Gaëtan Chenevier, Jean Lannes
    Pages 177-189
  9. Gaëtan Chenevier, Jean Lannes
    Pages 191-244
  10. Gaëtan Chenevier, Jean Lannes
    Pages 245-309
  11. Gaëtan Chenevier, Jean Lannes
    Pages 311-360
  12. Back Matter
    Pages 361-417

About this book

Introduction

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.

Keywords

automorphic forms unimodular lattices Kneser neighbors Niemeier lattices Arthur conjectures classical groups Galois representations Langlands conjectures L-functions quadratic forms Siegel modular forms Theta series

Authors and affiliations

  • Gaëtan Chenevier
    • 1
  • Jean Lannes
    • 2
  1. 1.CNRS, Institut de Mathématique d’OrsayUniversité Paris-SudOrsayFrance
  2. 2.Institut de Mathématiques de JussieuUniversité Paris DiderotParisFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-95891-0
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-95890-3
  • Online ISBN 978-3-319-95891-0
  • Series Print ISSN 0071-1136
  • Series Online ISSN 2197-5655
  • Buy this book on publisher's site
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