ENGLISH

Basic Analysis of Regularized Series and Products

By Serge Lang (auth.) , Jay A. Jorgenson

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1993
ISBN
3540574883, 9783540574880, 0387574883
DOI
10.1007/BFb0077194
LCC
QA3 .L28 no. 1564,QA241 .L28 no. 1564
Open Library ID
OL1427348M
Language
english
Format
DJVU
Filesize
510 kB (521870 bytes)
Series
Lecture Notes in Mathematics 1564
Edition
1
Pages
130\130
Library
Kolxo3
DPI
300
Time added
2009-07-20 03:45:11
Number Theory; Analysis; Differential Geometry

Description

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.

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