Linear relations of zeroes of the zeta-function

D G Best, T S Trudgian

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9 Citations (Scopus)

Abstract

This article considers linear relations between the nontrivial zeroes of the Riemann zeta-function. The main application is an alternative disproof of Mertens' conjecture by showing that lim supx→∞M(x)x-1/2 ≥ 1.6383, and lim infx→∞M(x)x-1/2 ≤ -1.6383.
Original languageEnglish
Pages (from-to)2047-2058
Number of pages12
JournalMathematics of Computation
Volume84
Issue number294
DOIs
Publication statusPublished - 2015

Keywords

  • Linear relations of ordinates
  • Riemann zeta-function zeros

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