Two arguments that the nontrivial zeros of the Riemann zeta function are irrational

Details Two arguments that the nontrivial zeros of the Riemann zeta function are irrational Two arguments that the nontrivial zeros of the Riemann zeta function are irrational

2010-02-22

arxiv.org/abs/1002.4171v2

Mathematics

Number Theory

Some improvements added and misprints corrected. The red lines in Fig.1 and Fig.3 does not hide the circles. Added Fig. 6 and

Scientific paper

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.

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