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: Ramanujan's Theta Functions
  name:
    name part: Cooper, Shaun.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2017
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVIII, 687 p. 1 illus. online resource.
  abstract: Theta functions were studied extensively by Ramanujan. This book provides a systematic development of Ramanujan’s results and extends them to a general theory. The author’s treatment of the subject is comprehensive, providing a detailed study of theta functions and modular forms for levels up to 12. Aimed at advanced undergraduates, graduate students, and researchers, the organization, user-friendly presentation, and rich source of examples, lends this book to serve as a useful reference, a pedagogical tool, and a stimulus for further research. Topics, especially those discussed in the second half of the book, have been the subject of much recent research; many of which are appearing in book form for the first time. Further results are summarized in the numerous exercises at the end of each chapter.
  table of contents: Preface -- 0. Sum to Product Identities -- 1. Elliptic Functions -- 2. Transformations -- 3. Theta Functions -- 4. Levels 1, 2, 3, and 4: Jacobi's Inversion Theorem and Ramanujan's Alternative Theories -- 5. Level 5: The Rogers-Ramanujan Continued Fraction -- 6. Level 6: Ramanujan's Cubic Continued Fraction -- 7. Level 7 -- 8. Level 8: The Ramanujan-Gollnitz-Gordon Continued Fraction -- 9. Level 9 -- 10. Level 10: Ramanujan's Function k -- 11. Levels 11 and 23 -- 12. Level 12 -- 13. Hypergeometric Modular Transformations -- 14. Ramanujan's Series for 1/pi -- References.
  note: by Shaun Cooper.
  subject:
    topic: Mathematics
  subject:
    topic: Algebraic geometry
  subject:
    topic: Number theory
  subject:
    topic: Mathematics
  subject:
    topic: Number Theory
  subject:
    topic: Algebraic Geometry
  classification: QA241-247.5
  classification: 512.7
  related item:
    title info:
      title: Springer eBooks
  identifier: 9783319561721
  identifier: http://dx.doi.org/10.1007/978-3-319-56172-1
  record info:
    record creation date: 170612
    record change date: 20180102141812.0
    record identifier: 978-3-319-56172-1