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: Pseudodifferential Methods in Number Theory
  name:
    name part: Unterberger, André.
    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: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2018
    edition: 1st ed. 2018.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: VI, 173 p. online resource.
  abstract: Classically developed as a tool for partial differential equations, the analysis of operators known as pseudodifferential analysis is here regarded as a possible help in questions of arithmetic. The operators which make up the main subject of the book can be characterized in terms of congruence arithmetic. They enjoy a Eulerian structure, and are applied to the search for new conditions equivalent to the Riemann hypothesis. These consist in the validity of certain parameter-dependent estimates for a class of Hermitian forms of finite rank. The Littlewood criterion, involving sums of Möbius coeffcients, and the Weil so-called explicit formula, which leads to his positivity criterion, fit within this scheme, using in the first case Weyl's pseudodifferential calculus, in the second case Fuchs'. The book should be of interest to people looking for new possible approaches to the Riemann hypothesis, also to new perspectives on pseudodifferential analysis and on the way it combines with modular form theory. Analysts will have no diffculty with the arithmetic aspects, with which, save for very few exceptions, no previous acquaintance is necessary.
  table of contents: Introduction - The basic tools -- Some measures and distributions in the plane -- Pseudodifferential arithmetic and Euler decompositions -- The role of modular forms -- Line measures and modular distributions -- Arithmetic and the Fuchs calculus -- A possible approach to the Riemann hypothesis?
  note: by André Unterberger.
  subject:
    topic: Number theory
  subject:
    topic: Partial differential equations
  subject:
    topic: Number Theory
  subject:
    topic: Partial Differential Equations
  classification: QA241-247.5
  classification: 512.7
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Pseudo-Differential Operators, Theory and Applications, 13
  identifier: 9783319927077
  identifier: https://doi.org/10.1007/978-3-319-92707-7
  record info:
    record creation date: 180716
    record change date: 20191028202608.0
    record identifier: 978-3-319-92707-7