On the zeros of linear combinations of derivatives of the Riemann zeta function

K. Paolina Koutsaki; Albert Tamazyan; Alexandru Zaharescu

doi:10.1142/S1793042116501049

On the zeros of linear combinations of derivatives of the Riemann zeta function

K. Paolina Koutsaki, Albert Tamazyan, Alexandru Zaharescu

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, the zeros of linear combinations of the Riemann zeta function and its derivatives are studied. We establish an asymptotic formula for the number of zeros in a rectangle of height T. We also find a sharp asymptotic formula for the supremum of the real parts of zeros of such combinations in a certain family.

Original language	English (US)
Pages (from-to)	1703-1723
Number of pages	21
Journal	International Journal of Number Theory
Volume	12
Issue number	6
DOIs	https://doi.org/10.1142/S1793042116501049
State	Published - Sep 1 2016

Keywords

Riemann zeta function
linear combination of derivatives
non-real zeros

ASJC Scopus subject areas

Algebra and Number Theory

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KW - linear combination of derivatives

KW - non-real zeros

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