Value Distribution of L-Functions (Lecture Notes in Mathematics) 〈Vol. 1877〉

Steuding, Jörn

Springer（2007/06発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 317 p.
• 商品コード 9783540265269

基本説明

These notes present recent results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality.

Full 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.

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.