Linear relations of zeroes of the zeta-function

Darcy Best; Tim Trudgian

arXiv:1209.3843·math.NT·July 2, 2015·Math. Comput.·1 cites

Linear relations of zeroes of the zeta-function

Darcy Best, Tim Trudgian

PDF

Open Access

TL;DR

None

Contribution

None

Abstract

This article considers linear relations between the non-trivial zeroes of the Riemann zeta-function. The main application is an alternative disproof to Mertens' conjecture. We show that $lim sup M (x) x^{- 1/2} \geq 1.6383$ and that $lim inf M (x) x^{- 1/2} \leq - 1.6383$ .

Peer Reviews

No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.

Videos

No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.

Taxonomy

TopicsAlgebraic Geometry and Number Theory · Analytic Number Theory Research · Meromorphic and Entire Functions