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  • © 1993

Basic Analysis of Regularized Series and Products

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1564)

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Table of contents (2 chapters)

  1. Front Matter

    Pages I-V
  2. Back Matter

    Pages 119-122

About this book

Analytic number theory and part of the spectral theory of operators (differential, pseudo-differential, elliptic, etc.) are being merged under amore general analytic theory of regularized products of certain sequences satisfying a few basic axioms. The most basic examples consist of the sequence of natural numbers, the sequence of zeros with positive imaginary part of the Riemann zeta function, and the sequence of eigenvalues, say of a positive Laplacian on a compact or certain cases of non-compact manifolds. The resulting theory is applicable to ergodic theory and dynamical systems; to the zeta and L-functions of number theory or representation theory and modular forms; to Selberg-like zeta functions; andto the theory of regularized determinants familiar in physics and other parts of mathematics. Aside from presenting a systematic account of widely scattered results, the theory also provides new results. One part of the theory deals with complex analytic properties, and another part deals with Fourier analysis. Typical examples are given. This LNM provides basic results which are and will be used in further papers, starting with a general formulation of Cram r's theorem and explicit formulas. The exposition is self-contained (except for far-reaching examples), requiring only standard knowledge of analysis.

Keywords

  • Modular form
  • Number theory
  • analysis
  • differential geometry
  • dynamical systems
  • ergodic theory
  • fourier analysis
  • regularized products and series
  • spectral theory

Bibliographic Information

  • Book Title: Basic Analysis of Regularized Series and Products

  • Authors: Jay A. Jorgenson, Serge Lang

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0077194

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1993

  • Softcover ISBN: 978-3-540-57488-0Published: 29 November 1993

  • eBook ISBN: 978-3-540-48193-5Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 130

  • Topics: Number Theory, Analysis, Differential Geometry

Buying options

eBook USD 29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 39.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions