| Value-Distribution of L-Functions 2007 Edition Contributor(s): Steuding, Jörn (Author) |
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ISBN: 3540265260 ISBN-13: 9783540265269 Publisher: Springer OUR PRICE: $66.49 Product Type: Paperback - Other Formats Published: June 2007 Annotation: These notes present recent results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality. In 1975, Voronin proved that any non-vanishing analytic function can be approximated uniformly by certain shifts of the Riemann zeta-function in the critical strip. This spectacular universality property has a strong impact on the zero-distribution: Riemann's hypothesis is true if and only if the Riemann zeta-function can approximate itself uniformly (in the sense of Voronin). Meanwhile universality is proved for a large zoo of Dirichlet series, and it is conjectured that all reasonable L-functions are universal. In these notes we prove universality for polynomial Euler products. Our approach follows mainly Bagchi's probabilistic method. We further discuss related topics as, e.g., almost periodicity, density estimates, Nevanlinna theory, and functional independence. |
| Additional Information |
| BISAC Categories: - Mathematics | Number Theory - Mathematics | Functional Analysis - Mathematics | Probability & Statistics - General |
| Dewey: 515.982 |
| Series: Lecture Notes in Mathematics |
| Physical Information: 0.79" H x 6.36" W x 9.3" (1.13 lbs) 322 pages |
| Descriptions, Reviews, Etc. |
| Publisher 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. |