New Computations of the Riemann Zeta Function on the Critical Line

Jonathan W. Bober, Ghaith A. Hiary*

*Corresponding author for this work

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

3 Citations (Scopus)
307 Downloads (Pure)

Abstract

We present highlights of computations of the Riemann zeta function around large values and high zeros. The main new ingredient in these computations is an implementation of the second author's fast algorithm for numerically evaluating quadratic exponential sums. In addition, we use a new simple multi-evaluation method to compute the zeta function in a very small range at little more than the cost of evaluation at a single point.
Original languageEnglish
Pages (from-to)125-137
Number of pages13
JournalExperimental Mathematics
Volume27
Issue number2
Early online date14 Oct 2016
DOIs
Publication statusPublished - 3 Apr 2018

Keywords

  • exponential sums
  • large values
  • the Riemann zeta function
  • the van der Corput iteration
  • theta algorithm

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