rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Automorphic Forms and Even Unimodular Lattices
    sub title: Kneser Neighbors of Niemeier Lattices
  name:
    name part: Chenevier, Gaëtan.
    role:
      role term: creator
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: Lannes, Jean.
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2019
    edition: 1st ed. 2019.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXI, 417 p. 24 illus., 1 illus. in color. online resource.
  abstract: 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.
  table of contents: Preface.-1 Introduction -- 2 Bilinear and Quadratic Algebra -- 3 Kneser Neighbors -- 4 Automorphic Forms and Hecke Operators -- 5 Theta Series and Even Unimodular Lattices -- 6 Langlands Parametrization -- 7 A Few Cases of the Arthur-Langlands Conjecture -- 8 Arthur's Classification for the Classical Z-groups -- 9 Proofs of the Main Theorems -- 10 Applications -- A The Barnes-Wall Lattice and the Siegel Theta Series -- B Quadratic Forms and Neighbors in Odd Dimension -- C Tables -- References.-.Postface- Notation Index.-Terminology Index.
  note: by Gaëtan Chenevier, Jean Lannes.
  subject:
    topic: Number theory
  subject:
    topic: Algebra
  subject:
    topic: Discrete mathematics
  subject:
    topic: Number Theory
  subject:
    topic: Algebra
  subject:
    topic: Discrete Mathematics
  classification: QA241-247.5
  classification: 512.7
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 69
  identifier: 9783319958910
  identifier: https://doi.org/10.1007/978-3-319-95891-0
  record info:
    record creation date: 190228
    record change date: 20191025062405.0
    record identifier: 978-3-319-95891-0