A method for verifying the generalized Riemann hypothesis

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 12 Sep 2025Embargo end date: 01 Aug 2024 English Publisher:American Mathematical Society (AMS)Journal:Mathematics of Computation (issn: 0025-5718, eissn: 1088-6842,

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Authors: Hiary, Ghaith; Ireland, Summer; Kyi, Megan;

doi: 10.1090/mcom/4129 , 10.48550/arxiv.2408.00187

arXiv: 2408.00187

A method for verifying the generalized Riemann hypothesis

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Abstract

Riemann numerically approximated at least three zeta zeros. According to Edwards, Riemann even took steps to verify that the lowest zero he computed was indeed the first zeta zero. This approach to verification is developed, improved, and generalized to a large class of $L$-functions. Results of numerical calculations demonstrating the efficacy of the method are presented.

28 pages, 3 figures

Keywords

11M06, 11Y35, Mathematics - Number Theory, FOS: Mathematics, Number Theory (math.NT)

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