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: Introduction to Modern Number Theory
    sub title: Fundamental Problems, Ideas and Theories
  name:
    name part: Manin, Yuri Ivanovic.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Panchishkin, Alexei A.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2005
    edition: 2.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVI, 514 p. online resource.
  abstract: "Introduction to Modern Number Theory" surveys from a unified point of view both the modern state and the trends of continuing development of various branches of number theory. Motivated by elementary problems, the central ideas of modern theories are exposed. Some topics covered include non-Abelian generalizations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories. Moreover, the authors have added a part dedicated to arithmetical cohomology and noncommutative geometry, a report on point counts on varieties with many rational points, the recent polynomial time algorithm for primality testing, and some others subjects. From the reviews of the 2nd edition: "… For my part, I come to praise this fine volume. This book is a highly instructive read … the quality, knowledge, and expertise of the authors shines through. … The present volume is almost startlingly up-to-date ..." (A. van der Poorten, Gazette, Australian Math. Soc. 34 (1), 2007).
  table of contents: Problems and Tricks -- Number Theory -- Some Applications of Elementary Number Theory -- Ideas and Theories -- Induction and Recursion -- Arithmetic of algebraic numbers -- Arithmetic of algebraic varieties -- Zeta Functions and Modular Forms -- Fermat’s Last Theorem and Families of Modular Forms -- Analogies and Visions -- Introductory survey to part III: motivations and description -- Arakelov Geometry and Noncommutative Geometry (d’après C. Consani and M. Marcolli, [CM]).
  note: by Yuri Ivanovic Manin, Alexei A. Panchishkin.
  subject:
    topic: Mathematics
  subject:
    topic: Data encryption (Computer science)
  subject:
    topic: Algebraic geometry
  subject:
    topic: Mathematical logic
  subject:
    topic: Number theory
  subject:
    topic: Physics
  subject:
    topic: Mathematics
  subject:
    topic: Number Theory
  subject:
    topic: Algebraic Geometry
  subject:
    topic: Mathematical Logic and Foundations
  subject:
    topic: Mathematical Methods in Physics
  subject:
    topic: Data Encryption
  subject:
    topic: Numerical and Computational Physics
  classification: QA241-247.5
  classification: 512.7
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Encyclopaedia of Mathematical Sciences, 49
  identifier: 9783540276920
  identifier: http://dx.doi.org/10.1007/3-540-27692-0
  record info:
    record creation date: 130729
    record change date: 20151204184541.0
    record identifier: 978-3-540-27692-0