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

Marek Wolf

Arxiv ID: 1002.4171•Last updated: 3/24/2020

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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