Opuscula Mathematica

Opuscula Math.
 24
, no. 1
 (), 103-114
Opuscula Mathematica

Li's criterion for the Riemann hypothesis - numerical approach


Abstract. There has been some interest in a criterion for the Riemann hypothesis proved recently by Xian-Jin Li [Li X.-J.: The Positivity of a Sequence of Numbers and the Riemann Hypothesis. J. Number Theory 65 (1997), 325-333]. The present paper reports on a numerical computation of the first 3300 of Li's coefficients which appear in this criterion. The main empirical observation is that these coefficients can be separated in two parts. One of these grows smoothly while the other is very small and oscillatory. This apparent smallness is quite unexpected. If it persisted till infinity then the Riemann hypothesis would be true.
Keywords: Riemann zeta function, Riemann hypothesis, Li's criterion, numerical methods in analytic number theory.
Mathematics Subject Classification: 11M26, 11Y60.
Cite this article as:
Krzysztof Maślanka, Li's criterion for the Riemann hypothesis - numerical approach, Opuscula Math. 24, no. 1 (2004), 103-114
 
Download this article's citation as:
a .bib file (BibTeX), a .ris file (RefMan), a .enw file (EndNote)
or export to RefWorks.

RSS Feed

horizontal rule

ISSN 1232−9274, e-ISSN 2300−6919, DOI http://dx.doi.org/10.7494/OpMath
Copyright © 2003−2017 OPUSCULA MATHEMATICA
Contact: opuscula@agh.edu.pl
Made by Tomasz Zabawa

horizontal rule

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.