## On the number of zeros and poles of Dirichlet series

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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.## References

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## Additional Information

**Bao Qin Li**- Affiliation: Department of Mathematics and Statistics, Florida International University, Miami, Florida 33199
- MR Author ID: 249034
- Email: libaoqin@fiu.edu
- Received by editor(s): May 2, 2016
- Received by editor(s) in revised form: August 28, 2016
- Published electronically: February 21, 2018
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**370**(2018), 3865-3883 - MSC (2010): Primary 30B50, 11M41, 11M36
- DOI: https://doi.org/10.1090/tran/7084
- MathSciNet review: 3811512