Computational estimation of the order of

Author:
Tadej Kotnik

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

Published electronically:
July 14, 2003

MathSciNet review:
2031417

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The paper describes a search for increasingly large extrema (ILE) of in the range . For , the complete set of ILE (57 of them) was determined. In total, 162 ILE were found, and they suggest that . 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:
tadej.kotnik@fe.uni-lj.si

DOI:
https://doi.org/10.1090/S0025-5718-03-01568-0

Keywords:
Riemann's zeta function,
critical line,
Lindel\"{o}f's hypothesis

Received by editor(s):
April 24, 2002

Received by editor(s) in revised form:
October 21, 2002

Published electronically:
July 14, 2003

Article copyright:
© Copyright 2003
American Mathematical Society