On the zero-free region and the distribution of zeros of the prime zeta function

Igoris Belovas; Rugilė Čepaitytė; Martynas Sabaliauskas

doi:10.2478/auom-2025-0017

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On the zero-free region and the distribution of zeros of the prime zeta function

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 33 (2025): Issue 2 (June 2025)

By: Igoris Belovas, Rugilė Čepaitytė and Martynas Sabaliauskas

Open Access

|Jun 2025

Abstract

The prime zeta function is one of the most under-researched varieties of the class. Very little is known about the irregular distribution of its zeros. The presented study aims - albeit partially - to fill the gap in our understanding of the subject. We consider the zero-free region of the prime zeta function and verify statistically certain conjectures regarding the distribution patterns of the zeroes of the prime zeta function.

References

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Articles in this issue

DOI: https://doi.org/10.2478/auom-2025-0017 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

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Language: English

Page range: 27 - 44

Submitted on: Oct 7, 2024

Accepted on: Feb 28, 2025

Published on: Jun 3, 2025

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

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© 2025 Igoris Belovas, Rugilė Čepaitytė, Martynas Sabaliauskas, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 33 (2025): Issue 2 (June 2025)