On the Distribution Modulo one of the a-Points of the k th Derivative of an L-Function in the Selberg Class

Mohammed Mekkaoui; Kamel Mazhouda

doi:10.2478/udt-2024-0003

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On the Distribution Modulo one of the a-Points of the k th Derivative of an L-Function in the Selberg Class

Uniform distribution theory

Volume 19 (2024): Issue 1-2 (December 2024)

By: Mohammed Mekkaoui and Kamel Mazhouda

Open Access

|Feb 2025

Abstract

Let F be an L-function from the Selberg class, F ^(k) be the kth derivative of F and a be an arbitrary fixed complex number. The solutions of F ^(k)(s)= a are called a-points. In this paper, we present a new zone without a-points of F ^(k) and we show that if F has a polynomial Euler product and satisfies the analogue of the Lindelöf hypothesis, then the a-points of F ^(k) are uniformly distributed modulo one.

References

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Articles in this issue

DOI: https://doi.org/10.2478/udt-2024-0003 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X

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Language: English

Page range: 15 - 32

Submitted on: Nov 9, 2023

Accepted on: Apr 13, 2024

Published on: Feb 24, 2025

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Riemann zeta function,

Related subjects:

Algebra and number theory,

Discrete mathematics,

Probability and statistics,

Numerical and computational mathematics

© 2025 Mohammed Mekkaoui, Kamel Mazhouda, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 19 (2024): Issue 1-2 (December 2024)