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Automorphic forms and even unimodula...

Chenevier, Gaetan.

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Automorphic forms and even unimodular lattices = Kneser neighbors of Niemeier Lattices /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Automorphic forms and even unimodular lattices/ by Gaetan Chenevier, Jean Lannes.
Reminder of title:	Kneser neighbors of Niemeier Lattices /
Author:	Chenevier, Gaetan.
other author:	Lannes, Jean.
Published:	Cham :Springer International Publishing : : 2019.,
Description:	xxi, 417 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Automorphic forms. -
Online resource:	https://doi.org/10.1007/978-3-319-95891-0
ISBN:	9783319958910

Automorphic forms and even unimodular lattices = Kneser neighbors of Niemeier Lattices /
Chenevier, Gaetan.

Automorphic forms and even unimodular latticesKneser neighbors of Niemeier Lattices /[electronic resource] :by Gaetan Chenevier, Jean Lannes. - Cham :Springer International Publishing :2019. - xxi, 417 p. :ill., digital ;24 cm. - Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A series of modern surveys in mathematics,v.690071-1136 ;. - Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A series of modern surveys in mathematics ;v.69..

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.

ISBN: 9783319958910

Standard No.: 10.1007/978-3-319-95891-0doiSubjects--Topical Terms:

576006
Automorphic forms.

LC Class. No.: QA353.A9

Dewey Class. No.: 515.9

Automorphic forms and even unimodular lattices = Kneser neighbors of Niemeier Lattices /
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100 1 $a Chenevier, Gaetan. $3 3385662
245 1 0 $a Automorphic forms and even unimodular lattices $h [electronic resource] : $b Kneser neighbors of Niemeier Lattices / $c by Gaetan Chenevier, Jean Lannes.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2019.
300 $a xxi, 417 p. : $b ill., digital ; $c 24 cm.
490 1 $a Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A series of modern surveys in mathematics, $x 0071-1136 ; $v v.69
520 $a 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.
650 0 $a Automorphic forms. $3 576006
650 0 $a Modular lattices. $3 3385664
650 1 4 $a Number Theory. $3 891078
650 2 4 $a Algebra. $3 516203
650 2 4 $a Discrete Mathematics. $3 1569938
700 1 $a Lannes, Jean. $3 709047
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A series of modern surveys in mathematics ; $v v.69. $3 3385663
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950 $a Mathematics and Statistics (Springer-11649)