## 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

## Abstract:

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.## References

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## Additional Information

**Tadej Kotnik**- Affiliation: Faculty of Electrical Engineering, University of Ljubljana, SI-1000 Ljubljana, Slovenia
- Email: tadej.kotnik@fe.uni-lj.si
- 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: https://doi.org/10.1090/S0025-5718-03-01568-0
- MathSciNet review: 2031417