Basic Analysis of Regularized Series and Products

Serge Lang

ISBN 10: 3540574883 / ISBN 13: 9783540574880

Published by Springer Berlin Heidelberg, 1993

About this Item

Druck auf Anfrage Neuware - Printed after ordering - Analytic number theory and part of the spectral theory ofoperators (differential, pseudo-differential, elliptic,etc.) are being merged under amore general analytic theoryof regularized products of certain sequences satisfying afew basic axioms. The most basic examples consist of thesequence of natural numbers, the sequence of zeros withpositive imaginary part of the Riemann zeta function, andthe sequence of eigenvalues, say of a positive Laplacian ona compact or certain cases of non-compact manifolds. Theresulting theory is applicable to ergodic theory anddynamical systems; to the zeta and L-functions of numbertheory or representation theory and modular forms; toSelberg-like zeta functions; andto the theory ofregularized determinants familiar in physics and other partsof mathematics. Aside from presenting a systematic accountof widely scattered results, the theory also provides newresults. One part of the theory deals with complex analyticproperties, and another part deals with Fourier analysis.Typical examples are given. This LNM provides basic resultswhich are and will be used in further papers, starting witha general formulation of Cram r's theorem and explicitformulas. The exposition is self-contained (except forfar-reaching examples), requiring only standard knowledge ofanalysis.

Seller Inventory # 9783540574880

Bibliographic Details

• Title: Basic Analysis of Regularized Series and Products
• Publisher: Springer Berlin Heidelberg
• Publication Date: 1993
• Language: English
• ISBN 10: 3540574883
• ISBN 13: 9783540574880
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 8D millimeters 235 millimeters width by 155 millimeters height by 8 millimeters depth
• Weight: 224 grams

About this title

Synopsis

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.