Accurate estimation of sums over zeros of the Riemann zeta-function
| Autor: | Richard P. Brent, Tim Trudgian, David J. Platt |
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| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Mathematics - Number Theory Accurate estimation Applied Mathematics 11M06 11M26 Interval (mathematics) Function (mathematics) Riemann zeta function Computational Mathematics Riemann hypothesis symbols.namesake Convergent and divergent production Simple (abstract algebra) FOS: Mathematics symbols Number Theory (math.NT) Numerical estimation Mathematics |
| Zdroj: | Mathematics of Computation. 90:2923-2935 |
| ISSN: | 1088-6842 0025-5718 |
| DOI: | 10.1090/mcom/3652 |
| Popis: | We consider sums of the form $\sum \phi(\gamma)$, where $\phi$ is a given function, and $\gamma$ ranges over the ordinates of nontrivial zeros of the Riemann zeta-function in a given interval. We show how the numerical estimation of such sums can be accelerated by a simple device, and give examples involving both convergent and divergent infinite sums. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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