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Automorphic forms and even unimodular lattices : Kneser neighbors of Niemeier lattices / Gaëtan Chenevier, Jean Lannes ; translated by Reinie Erné.
Author
Chenevier, Gaëtan
[Browse]
Uniform title
Formes automorphes et voisins de Kneser des réseaux de Niemeier.
English
[Browse]
Format
Book
Language
English
Published/Created
Cham, Switzerland : Springer, [2019]
©2019
Description
xxi, 417 pages : illustrations ; 25 cm
Availability
Available Online
Springer Nature - Springer Mathematics and Statistics eBooks 2019 English International
Copies in the Library
Location
Call Number
Status
Location Service
Notes
Lewis Library - Stacks
QA243 .C53 2019
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Details
Subject(s)
Automorphic forms
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Modular lattices
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Lattice theory
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Forms, Quadratic
[Browse]
Author
Lannes, Jean
[Browse]
Translator
Erné, Reinie
[Browse]
Series
Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, Bd. 69.
[More in this series]
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 0071-1136 ; volume 69
[More in this series]
Summary note
"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."--Provided by publisher.
Bibliographic references
Includes bibliographical references (pages 397-408) and indexes.
Language note
Translated from the French.
Contents
Bilinear and quadratic algebra
Kneser neighbors
Automorphic forms and Hecke operators
Theta series and even unimodular lattices
Langlands parametrization
A few cases of the Arthur-Langlands conjecture
Arthur's classification for the classical Z -groups
Proofs of the main theorems
Applications
A. The Barnes-Wall lattice and the Siegel theta series of even unimodular lattices of dimension 16
B. Quadratic forms and neighbors in odd dimension
C. Tables
Postface.
Show 10 more Contents items
ISBN
9783319958903 ((hardcover))
3319958909 ((hardcover))
OCLC
1039606065
Statement on language in description
Princeton University Library aims to describe library materials in a manner that is respectful to the individuals and communities who create, use, and are represented in the collections we manage.
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Automorphic Forms and Even Unimodular Lattices [electronic resource] : Kneser Neighbors of Niemeier Lattices / by Gaëtan Chenevier, Jean Lannes.
id
99125423714806421