Erdős-Macintyre type theorem’s for multiple Dirichlet series: exceptional sets and open problems

  • A. I. Bandura Ivano-Frankivsk National Technical University of Oil and Gas
  • T. M. Salo National University ``Lvivska Politekhnika''
  • O. B. Skaskiv Ivan Franko National University of Lviv, Lviv, Ukraine
Keywords: Wiman's inequality; Erd\H{o}s-Macintyre theorem; maximal term; maximum modulus; minimum modulus; exceptional set; Dirichlet series

Abstract

In the paper, we formulate some open problems related to the best description of the values of the exceptional sets in Wiman's inequality for entire functions and in the Erd\H{o}s-Macintyre type theorems for entire multiple Dirichlet series. At the same time, we clarify the statement of one \v{I}.V. Ostrovskii problem on Wiman's inequality. We also prove three propositions and one theorem. On the one hand, in a rather special case, these results give the best possible description of the values of the exceptional set in the Erd\H{o}s-Macintyre-type theorem. On the second hand, they indicate the possible structure of the best possible description in the general case.

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Published
2023-01-23
How to Cite
Bandura, A. I., Salo, T. M., & Skaskiv, O. B. (2023). Erdős-Macintyre type theorem’s for multiple Dirichlet series: exceptional sets and open problems. Matematychni Studii, 58(2), 212-221. https://doi.org/10.30970/ms.58.2.212-221
Section
Problem Section