On the first sign change of θ(x)-x

David J Platt, Tim Trudgian

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

23 Citations (Scopus)
301 Downloads (Pure)

Abstract

Let θ(x) = ∑pxlogp. We show that θ(x) < x for 2 < x < 1.39·1017. We also show that there is an x < exp(727.951332668) for which θ(x) > x.
Original languageEnglish
Pages (from-to)1539-1547
Number of pages9
JournalMathematics of Computation
Volume85
DOIs
Publication statusPublished - 21 Aug 2015

Keywords

  • Sign changes of arithmetical functions
  • oscillation theorems
  • HPC (High Performance Computing) Facility

    Sadaf R Alam (Manager), Steven A Chapman (Manager), Polly E Eccleston (Other), Simon H Atack (Other) & D A G Williams (Manager)

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