Automorphic Forms and Even Unimodular Lattices: Kneser Neighbors of Niemeier Lattices - Couverture rigide

Chenevier, Gaëtan; Lannes, Jean

Couverture rigide

ISBN 10 : 3319958909 ISBN 13 : 9783319958903

Editeur : Springer International Publishing AG, 2019

Synopsis

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.

A propos du livre

À propos de l'auteur

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.

Détails de l'édition

• Éditeur: Springer International Publishing AG
• Date d'édition: 2019
• Langue: anglais
• ISBN 10: 3319958909
• ISBN 13: 9783319958903
• Reliure: Relié
• Nombre de pages: 438
• Coordonnées du fabricant: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Allemagne