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Zeroes of partial sums of the zeta-function

Research output: Contribution to journalArticle

  • David J Platt
  • Timothy Trudgian
Original languageEnglish
Pages (from-to)37-41
Number of pages5
JournalLMS Journal of Computation and Mathematics
Volume19
Issue number1
DOIs
DateAccepted/In press - 11 Dec 2015
DatePublished (current) - 29 Feb 2016

Abstract

This article considers the positive integers N for which ζN(s)=∑Nn=1n−s has zeroes in the half-plane R(s)>1. Building on earlier results, we show that there are no zeroes for 1⩽N⩽18 and for N=20,21,28. For all other N there are infinitely many such zeroes.

    Research areas

  • 11M06 (primary), 11Y35 (secondary)

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