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

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Název: On the zero-free region and the distribution of zeros of the prime zeta function
Autoři: Belovas Igoris, Čepaitytė Rugilė, Sabaliauskas Martynas
Zdroj: Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, Vol 33, Iss 2, Pp 27-44 (2025)
Informace o vydavateli: Sciendo, 2025.
Rok vydání: 2025
Sbírka: LCC:Mathematics
Témata: prime zeta function, zeta function zeros, zero-free region, primary 11m41, secondary 11m99, Mathematics, QA1-939
Popis: 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.
Druh dokumentu: article
Popis souboru: electronic resource
Jazyk: English
ISSN: 1844-0835
Relation: https://doaj.org/toc/1844-0835
DOI: 10.2478/auom-2025-0017
Přístupová URL adresa: https://doaj.org/article/594ce6f5e4fb4a14baa5528a42a79e55
Přístupové číslo: edsdoj.594ce6f5e4fb4a14baa5528a42a79e55
Databáze: Directory of Open Access Journals
Popis
Abstrakt: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.
ISSN:18440835
DOI:10.2478/auom-2025-0017