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: Fractal geometry and number theory
    sub title: complex dimensions of fractal strings and zeros of zeta functions, with 26 illustrations
  name:
    name part: Lapidus, Michel L. (Michel Laurent)
    name part: 1956-
    role:
      role term: creator
  name:
    name part: Van Frankenhuysen, Machiel
    name part: 1967-
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: mau
    date issued: 2000
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: preservation
    reformatting quality: access
    form: remote
    extent: 1 online resource (x, 268 pages) : illustrations
  table of contents: 1 Complex Dimensions of Ordinary Fractal Strings -- 1.1 The Geometry of a Fractal String -- 1.2 The Geometric Zeta Function of a Fractal String -- 1.3 The Frequencies of a Fractal String and the Spectral Zeta Function -- 1.4 Higher-Dimensional Analogue: Fractal Sprays -- 2 Complex Dimensions of Self-Similar Fractal Strings -- 2.1 The Geometric Zeta Function of a Self-Similar String -- 2.2 Examples of Complex Dimensions of Self-Similar Strings -- 2.3 The Lattice and Nonlattice Case -- 2.4 The Structure of the Complex Dimensions -- 2.5 The Density of the Poles in the Nonlattice Case -- 2.6 Approximating a Fractal String and Its Complex Dimensions -- 3 Generalized Fractal Strings Viewed as Measures -- 3.1 Generalized Fractal Strings -- 3.2 The Frequencies of a Generalized Fractal String -- 3.3 Generalized Fractal Sprays -- 3.4 The Measure of a Self-Similar String -- 4 Explicit Formulas for Generalized Fractal Strings -- 4.1 Introduction -- 4.2 Preliminaries: The Heaviside Function -- 4.3 The Pointwise Explicit Formulas -- 4.4 The Distributional Explicit Formulas -- 4.5 Example: The Prime Number Theorem -- 5 The Geometry and the Spectrum of Fractal Strings -- 5.1 The Local Terms in the Explicit Formulas -- 5.2 Explicit Formulas for Lengths and Frequencies -- 5.3 The Direct Spectral Problem for Fractal Strings -- 5.4 Self-Similar Strings -- 5.5 Examples of Non-Self-Similar Strings -- 5.6 Fractal Sprays -- 6 Tubular Neighborhoods and Minkowski Measurability -- 6.1 Explicit Formula for the Volume of a Tubular Neighborhood -- 6.2 Minkowski Measurability and Complex Dimensions -- 6.3 Examples -- 7 The Riemann Hypothesis, Inverse Spectral Problems and Oscillatory Phenomena -- 7.1 The Inverse Spectral Problem -- 7.2 Complex Dimensions of Fractal Strings and the Riemann Hypothesis -- 7.3 Fractal Sprays and the Generalized Riemann Hypothesis -- 8 Generalized Cantor Strings and their Oscillations -- 8.1 The Geometry of a Generalized Cantor String -- 8.2 The Spectrum of a Generali…
  note: Michel L. Lapidus, Machiel van Frankenhuysen.
  note: Electronic resource.
  note: Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL
  note: digitized 2011 HathiTrust Digital Library committed to preserve pda MiAaHDL
  note: Includes bibliographical references and indexes.
  subject:
    topic: Fractals
  subject:
    topic: Number theory
  subject:
    topic: Functions, Zeta
  subject:
    topic: Fractales
  subject:
    topic: Nombres, Théorie des
  subject:
    topic: Fonctions zêta
  subject:
    topic: Fractals
  subject:
    topic: Functions, Zeta
  subject:
    topic: Number theory
  classification: QA614.86 .L36 2000
  classification: 514/.742
  related item:
    identifier: (DLC) 99051583
    identifier: (OCoLC)42641760
  identifier: 9781461253143 (electronic bk.)
  identifier: 1461253144 (electronic bk.)
  identifier: 0817640983 (acid-free paper)
  identifier: 9780817640989 (acid-free paper)
  identifier: 3764340983
  identifier: 9783764340988
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: OCLCE
    record creation date: 120929
    record change date: 20260420210850.6
    record identifier: in00003551328
    language of cataloging:
      language term: eng