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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On the number of zeros and poles of Dirichlet series
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by Bao Qin Li PDF
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.
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