On the number of zeros and poles of Dirichlet series

Li, Bao Qin

doi:10.1090/tran/7084

On the number of zeros and poles of Dirichlet series
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Trans. Amer. Math. Soc. 370 (2018), 3865-3883 Request permission

Abstract:

This paper investigates lower bounds on the number of zeros and poles of a general Dirichlet series in a disk of radius $r$ and gives, as a consequence, an affirmative answer to an open problem of Bombieri and Perelli on the bound. Applications will also be given to Picard type theorems, global estimates on the symmetric difference of zeros, and uniqueness problems for Dirichlet series.

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