Automorphic forms and even unimodular lattices : Kneser neighbors of Niemeier lattices / Gaëtan Chenevier, Jean Lannes ; translated by Reinie Erné.

Chenevier, Gaëtan [Browse]
  • Cham, Switzerland : Springer, [2019]
  • ©2019
xxi, 417 pages : illustrations ; 25 cm.


  • Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, Bd. 69. [More in this series]
  • Ergebnisse der Mathematik und ihrer Grenzgebiete = A series of modern surveys in mathematics ; 3. Folge, volume 69
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.
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.
  • 3319958909 ((hardcover))
  • 9783319958903 ((hardcover))
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