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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 /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Automorphic forms and even unimodular lattices/ by Gaetan Chenevier, Jean Lannes.
其他題名:	Kneser neighbors of Niemeier Lattices /
作者:	Chenevier, Gaetan.
其他作者:	Lannes, Jean.
出版者:	Cham :Springer International Publishing : : 2019.,
面頁冊數:	xxi, 417 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Automorphic forms. -
電子資源:	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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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.
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