Zeroes of partial sums of the zeta-function

David J Platt, Timothy Trudgian

Research output: Contribution to journalArticle (Academic Journal)peer-review

3 Citations (Scopus)
362 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)37-41
Number of pages5
JournalLMS Journal of Computation and Mathematics
Issue number1
Publication statusPublished - 29 Feb 2016


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


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