Two arguments that the nontrivial zeros of the Riemann zeta function are irrational
Number Theory
2020-03-24 v2 General Mathematics
Abstract
We have used the first 2600 nontrivial zeros gamma_l of the Riemann zeta function calculated with 1000 digits accuracy and developed them into the continued fractions. We calculated the geometrical means of the denominators of these continued fractions and for all cases we get values close to the Khinchin's constant, what suggests that gamma_l are irrational. Next we have calculated the n-th square roots of the denominators q_n of the convergents of the continued fractions obtaining values close to the Khinchin-Levy constant, again supporting the common believe that gamma_l are irrational.
Keywords
Cite
@article{arxiv.1002.4171,
title = {Two arguments that the nontrivial zeros of the Riemann zeta function are irrational},
author = {Marek Wolf},
journal= {arXiv preprint arXiv:1002.4171},
year = {2020}
}
Comments
Some improvements added and misprints corrected. The red lines in Fig.1 and Fig.3 does not hide the circles. Added Fig. 6 and some references