Two Arguments that the Nontrivial Zeros of the Riemann Zeta Function are Irrational. Part II

This is the authors' abstract. We don't add key points for this paper.

We extend the results of our previous computer experiment performed on the first 2600 nontrivial zeros γₗ of the Riemann zeta function calculated with 1000 digits accuracy to the set of 40000 first zeros given with 40000 decimal digits accuracy. We calculated the geometrical means of the denominators of continued fractions expansions of these zeros and for all cases we get values very close to the Khinchin's constant, which suggests that γₗ are irrational. Next we have calculated the n-th square roots of the denominators Qₙ of the convergents of the continued fractions obtaining values very close to the Khinchin---L{é}vy constant, again supporting the common opinion that γₗ are irrational.