Automorphic Forms and Even Unimodular Lattices - Kneser Neighbors of Niemeier Lattices (Hardcover, 1st ed. 2019)

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.

General

Imprint:	Springer International Publishing AG
Country of origin:	Switzerland
Series:	Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 69
Release date:	March 2019
First published:	2019
Translators:	Reinie Erne
Authors:	Gaetan Chenevier • Jean Lannes
Dimensions:	235 x 155 x 32mm (L x W x T)
Format:	Hardcover
Pages:	417
Edition:	1st ed. 2019
ISBN-13:	978-3-319-95890-3
Categories:	Books > Science & Mathematics > Mathematics > Algebra > General Books > Science & Mathematics > Mathematics > Number theory > General
LSN:	3-319-95890-9
Barcode:	9783319958903

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