A class of approximations to the Riemann zeta function

DOI10.1016/J.JMAA.2022.126344zbMath1496.11117OpenAlexW4280572966MaRDI QIDQ2147833

Alexandru Zaharescu, Maria Năstăsescu

Publication date: 20 June 2022

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2022.126344

zbMATH Keywords

Riemann zeta functiondistribution of zeros

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06)

Cites Work

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• A hybrid Euler-Hadamard product for the Riemann zeta function
• A few factors from the Euler product are sufficient for calculating the zeta function with high precision
• More than one third of zeros of Riemann's zeta-function are on \(\sigma=1/2\)
• More than five-twelfths of the zeros of \(\zeta\) are on the critical line
• Mean values of finite Euler products
• More than two fifths of the zeros of the Riemann zeta function are on the critical line.
• Finite Euler products and the Riemann hypothesis

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