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On the number of zeros and poles of Dirichlet series


Author: Bao Qin Li
Journal: Trans. Amer. Math. Soc. 370 (2018), 3865-3883
MSC (2010): Primary 30B50, 11M41, 11M36
DOI: https://doi.org/10.1090/tran/7084
Published electronically: February 21, 2018
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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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Additional Information

Bao Qin Li
Affiliation: Department of Mathematics and Statistics, Florida International University, Miami, Florida 33199
Email: libaoqin@fiu.edu

DOI: https://doi.org/10.1090/tran/7084
Keywords: General Dirichlet series, meromorphic function, zero, pole, counting function, L-function
Received by editor(s): May 2, 2016
Received by editor(s) in revised form: August 28, 2016
Published electronically: February 21, 2018
Article copyright: © Copyright 2018 American Mathematical Society

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