Value-Distribution of L-FunctionsSpringer Science & Business Media, 2007年6月6日 - 317页 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. |
目录
Dirichlet Series and Polynomial Euler Products 35 | 34 |
Results from Probability Theory | 49 |
Limit Theorems 63 | 62 |
Universality | 87 |
The Selberg Class | 111 |
ValueDistribution in the Complex Plane 137 | 136 |
The Riemann Hypothesis | 155 |
Effective Results | 167 |
Consequences of Universality 193 | 192 |
Dirichlet Series with Periodic Coefficients | 209 |
A Short History of Universality | 285 |
| 292 | |
Notations | 311 |
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常见术语和短语
absolute convergence algebraic analytic continuation analytic function approximation arithmetic Artin L-functions assume automorphic axioms Bagchi bounded c-values coefficients compact subset complex numbers connected complement continuous function converges weakly critical line critical strip Dedekind zeta-functions defined denote dense density Dirichlet L-functions Dirichlet series distribution estimate Euler factors Euler product finite follows function g(s functional equation Galois Hecke L-functions Hence Hurwitz zeta-functions implies independent joint universality Laurinčikas Lemma lim inf lim sup limit theorem Lindelöf hypothesis log log Math Matsumoto mean-square meas multiplicative Murty newforms non-trivial zeros non-vanishing number fields number theory obtain Perelli polynomial Euler product positive integer prime number theorem probability measure proof of Theorem proved Ramanujan hypothesis random element real number representation result Riemann hypothesis Riemann zeta-function satisfying Sect Selberg class Selberg's Conjecture space Steuding uniformly value-distribution values Voronin's universality theorem zeta ΣΣ