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  Lower bounds for discrete negative moments of the Riemann zeta function

Heap, W. P., Li, J., & Zhao, J. (2022). Lower bounds for discrete negative moments of the Riemann zeta function. Algebra & Number Theory, 16(7), 1589-1625. doi:10.2140/ant.2022.16.1589.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0009-FFF9-0 Version Permalink: https://hdl.handle.net/21.11116/0000-000E-12FE-0
Genre: Journal Article

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Heap-Li-Zhao_Lower bounds for discrete negative moments of the Riemann zeta function_2022.pdf (Publisher version), 490KB
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Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer Allianz- bzw. Nationallizenz frei zugänglich. / This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence respectively.
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https://doi.org/10.2140/ant.2022.16.1589 (Publisher version)
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 Creators:
Heap, Winston P.1, Author           
Li, Junxian1, Author           
Zhao, Jing1, Author           
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Number Theory
 Abstract: We prove lower bounds for the discrete negative $2k$th moment of the derivative of the Riemann zeta function for all fractional $k\geqslant 0$. The bounds are in line with a conjecture of Gonek and Hejhal. Along the way, we prove a general formula for the discrete twisted second moment of the Riemann zeta function. This agrees with a conjecture of Conrey and Snaith.

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Language(s): eng - English
 Dates: 2022
 Publication Status: Issued
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 Rev. Type: Peer
 Identifiers: arXiv: 2003.09368
DOI: 10.2140/ant.2022.16.1589
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Title: Algebra & Number Theory
Source Genre: Journal
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Publ. Info: Mathematical Sciences Publishers (MSP)
Pages: - Volume / Issue: 16 (7) Sequence Number: - Start / End Page: 1589 - 1625 Identifier: -