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Basic Analysis of Regularized Series and Products
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Basic Analysis of Regularized Series and Products (Paperback)

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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.

Science & MathematicsMathematicsCalculus & mathematical analysisScience & MathematicsMathematicsNumber theory Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Publication Date: 29/11/1993 ISBN-13: 9783540574880  Details: Type: Paperback Format: Books
Availability: Printed to order. Despatched in 2-3 weeks.  

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