Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On Some Sums at the a-points of Derivatives of the Riemann Zeta-Function

  • Kamel Mazhouda (University of Sousse, Higher Institute of Applied Sciences and Technology) ;
  • Tomokazu Onozuka (Multiple Zeta Research Center, Kyushu University)
  • Received : 2023.09.30
  • Accepted : 2023.06.12
  • Published : 2024.09.30
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Abstract

Let ζ(k)(s) be the k-th derivative of the Riemann zeta function and a be a complex number. The solutions of ζ(k)(s) = a are called a-points. In this paper, we give an asymptotic formula for the sum $$\sum_{1<{\gamma}_a^{(k)}, where j and k are non-negative integers and ρ(k)a denotes an a-point of the k-th derivative ζ(k)(s) and γ(k)a = Im(ρ(k)a).

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Acknowledgement

The authors thank the anonymous referee for his careful reading of the manuscript and constructive suggestions which improved the paper.

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