On the Montgomery–Odlyzko method regarding gaps between zeros of the zeta-function

Publication Date

11-15-2023

Document Type

Article

Publication Title

Journal of Mathematical Analysis and Applications

Volume

527

Issue

2

DOI

10.1016/j.jmaa.2023.127548

Abstract

Assuming the Riemann Hypothesis, it is known that there are infinitely many consecutive pairs of zeros of the Riemann zeta-function within 0.515396 times the average spacing. This is obtained using the method of Montgomery and Odlyzko. We prove that this method can never find infinitely many pairs of consecutive zeros within 0.5042 times the average spacing.

Funding Number

DMS-1854398

Funding Sponsor

National Science Foundation

Keywords

Riemann zeta-function, Vertical distribution of zeros

Department

Mathematics and Statistics

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