Value-distribution of L-functions
Author(s)
Bibliographic Information
Value-distribution of L-functions
（Lecture notes in mathematics, 1877）
Springer, c2007
Available at / 58 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||1877200001578156
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Note
Includes bibliographical references (p. [293]-309) and index
Description and Table of Contents
Description
These notes present recent results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality. Universality has a strong impact on the zero-distribution: Riemann's hypothesis is true only if the Riemann zeta-function can approximate itself uniformly. The text proves universality for polynomial Euler products. The authors' approach follows mainly Bagchi's probabilistic method. Discussion touches on related topics: almost periodicity, density estimates, Nevanlinna theory, and functional independence.
Table of Contents
Dirichlet Series and Polynomial Euler Products.- Interlude: Results from Probability Theory.- Limit Theorems.- Universality.- The Selberg Class.- Value-Distribution in the Complex Plane.- The Riemann Hypothesis.- Effective Results.- Consequences of Universality.- Dirichlet Series with Periodic Coefficients.- Joint Universality.- L-Functions of Number Fields.
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