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Zeros and poles of Dirichlet series

Enrico Bombieri, Alberto Perelli (2001)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Under certain mild analytic assumptions one obtains a lower bound, essentially of order r , for the number of zeros and poles of a Dirichlet series in a disk of radius r . A more precise result is also obtained under more restrictive assumptions but still applying to a large class of Dirichlet series.

Zeros of Sequences of Partial Sums and Overconvergence

Kovacheva, Ralitza K. (2008)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 30B40, 30B10, 30C15, 31A15.We are concerned with overconvergent power series. The main idea is to relate the distribution of the zeros of subsequences of partial sums and the phenomenon of overconvergence. Sufficient conditions for a power series to be overconvergent in terms of the distribution of the zeros of a subsequence are provided, and results of Jentzsch-Szegö type about the asymptotic distribution of the zeros of overconvergent subsequences are stated....

Zeta functions for the Riemann zeros

André Voros (2003)

Annales de l’institut Fourier

A family of Zeta functions built as Dirichlet series over the Riemann zeros are shown to have meromorphic extensions in the whole complex plane, for which numerous analytical features (the polar structures, plus countably many special values) are explicitly displayed.

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