Two Arguments that the Nontrivial Zeros of the Riemann Zeta Function are Irrational. Part 2

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 40 000 first zeros given with 40 000 decimal digits accuracy. We calculated the geometric 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-Lévy constant, again supporting the common opinion that γl are irrational.

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Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).