Computational estimation of the order of <IMG BORDER="0" SRC="/mcom/2004-73-246/S0025-5718-03-01568-0/gif-title0/img1.gif" >期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Computational estimation of the order of

Authors:	Tadej Kotnik.

Affiliation:	Faculty of Electrical Engineering, University of Ljubljana, SI-1000 Ljubljana, Slovenia

Abstract:	The paper describes a search for increasingly large extrema (ILE) of $leftvert zeta (frac{1}{2}+it)rightvert$ in the range $0leq tleq 10^{13}$ . For $tleq 10^{6}$ , 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.

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

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