Lower bounds for discrete negative moments of the Riemann zeta function

Heap, Winston P.; Li, Junxian; Zhao, Jing

doi:10.2140/ant.2022.16.1589

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsRelease HistoryDetailsSummary

Released

Journal Article

Lower bounds for discrete negative moments of the Riemann zeta function

MPS-Authors

/persons/resource/persons255482

Heap, Winston P.
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons247356

Li, Junxian
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons255485

Zhao, Jing
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.2140/ant.2022.16.1589
(Publisher version)

https://doi.org/10.48550/arXiv.2003.09368
(Preprint)

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

Fulltext (public)

Heap-Li-Zhao_Lower bounds for discrete negative moments of the Riemann zeta function_2022.pdf
(Publisher version), 490KB

MPIM Preprint series 2020-20.pdf
(Preprint), 488KB

Supplementary Material (public)

There is no public supplementary material available

Citation

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.

Cite as: https://hdl.handle.net/21.11116/0000-0009-FFF9-0

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.