Bootstrapped zero density estimates and a central limit theorem for the zeros of the zeta function
| Autor: | Kenneth Maples, Brad Rodgers |
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| Rok vydání: | 2015 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Mathematics - Number Theory Probability (math.PR) Zero (complex analysis) Riemann zeta function symbols.namesake Riemann hypothesis Simple (abstract algebra) FOS: Mathematics symbols sort Number Theory (math.NT) Random matrix Mathematics - Probability Eigenvalues and eigenvectors Central limit theorem Mathematics |
| Zdroj: | International Journal of Number Theory. 11:2087-2107 |
| ISSN: | 1793-7310 1793-0421 |
| DOI: | 10.1142/s1793042115500918 |
| Popis: | We unconditionally prove a central limit theorem for linear statistics of the zeros of the Riemann zeta function with diverging variance. Previously, theorems of this sort have been proved under the assumption of the Riemann hypothesis. The result mirrors central limit theorems in random matrix theory that have been proved by Szeg\H{o}, Spohn, and Soshnikov among others, and therefore provides support for the view that the zeros of the zeta function are distributed like the eigenvalues of a random matrix. A key ingredient in our proof is a simple bootstrapping of classical zero density estimates of Selberg and Jutila for the zeta function, which may be of independent interest. Comment: 19 pages. Incorporates referees suggestions |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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