Automorphic Forms and Even Unimodular Lattices Kneser Neighbors of N
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 recen
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Gaëtan Chenevier Jean Lannes
Automorphic Forms and Even Unimodular Lattices Kneser Neighbors of Niemeier Lattices
Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge
A Series of Modern Surveys in Mathematics
Editorial Board L. Ambrosio, Pisa V. Baladi, Paris G.-M. Greuel, Kaiserslautern M. Gromov, Bures-sur-Yvette G. Huisken, T¨ ubingen J. Jost, Leipzig J. Kollár, Princeton G. Laumon, Orsay U. Tillmann, Oxford J. Tits, Paris D.B. Zagier, Bonn
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Volume 69
Gaëtan Chenevier • Jean Lannes
Automorphic Forms and Even Unimodular Lattices Kneser Neighbors of Niemeier Lattices
Translated by Reinie Erné
123
Gaëtan Chenevier CNRS, Institut de Mathématique d’Orsay Université Paris-Sud Orsay, France
Jean Lannes Institut de Mathématiques de Jussieu Université Paris Diderot Paris, France
ISSN 0071-1136 ISSN 2197-5655 (electronic) Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics ISBN 978-3-319-95890-3 ISBN 978-3-319-95891-0 (eBook) https://doi.org/10.1007/978-3-319-95891-0 Library of Congress Control Number: 2018963583 Mathematics Subject Classification (2010): 11E, 11F, 11H, 11M, 11R, 11E12, 11F27, 11F46, 11F55, 11F60, 11F66, 11F80, 11H06, 11H55, 11R39 © Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
Automorphic forms are functions defined on adele groups, derived from harmonic analysis, whose theory forms a far-reaching generalization of that of modular forms. Langlands’ famous functoriality conjecture predicts unexpected connections between automorphic forms associated with quite different groups. Recent advances confirm part of these general conje
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