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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Computational estimation of the order of $\zeta (\frac {1}{2}+it)$
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by Tadej Kotnik PDF
Math. Comp. 73 (2004), 949-956 Request permission


The paper describes a search for increasingly large extrema (ILE) of $\left | \zeta (\frac {1}{2}+it)\right |$ in the range $0\leq t\leq 10^{13}$. For $t\leq 10^{6}$, the complete set of ILE (57 of them) was determined. In total, 162 ILE were found, and they suggest that $\zeta (\frac {1}{2} +it)=\Omega (t^{2/\sqrt {\log t \log \log t}})$. There are several regular patterns in the location of ILE, and arguments for these regularities are presented. The paper concludes with a discussion of prospects for further computational progress.
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Additional Information
  • Tadej Kotnik
  • Affiliation: Faculty of Electrical Engineering, University of Ljubljana, SI-1000 Ljubljana, Slovenia
  • Email:
  • Received by editor(s): April 24, 2002
  • Received by editor(s) in revised form: October 21, 2002
  • Published electronically: July 14, 2003
  • © Copyright 2003 American Mathematical Society
  • Journal: Math. Comp. 73 (2004), 949-956
  • MSC (2000): Primary 11M06, 11Y60; Secondary 11Y35, 65A05
  • DOI:
  • MathSciNet review: 2031417