2010/02/28 by Marek Wolf
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics #Computer science #Constant (computer programming) #Function (biology) #Geometry #History and Theory of Mathematics #Irrational number #Mathematical analysis #Mathematical physics #Mathematics #Number theory #Pure mathematics #Riemann hypothesis #Riemann zeta function #math.GM #math.NT
paper · pdf · doi:10.12921/cmst.2018.0000049
published as Computational Methods in Science and Technology Volume 24 (4) pp. 215--220, (2018) · 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
arxiv created 2010/02/28 · openalex publication_date 2018/01/01 · arxiv updated 2020/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We have used the first 2600 nontrivial zeros 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, which suggests that l are irrational. Next we have calculated the n-th square roots of the denominators Qn of the convergents of the continued fractions obtaining values close to the Khinchin-Lvy constant, again supporting the common opinion that l are irrational.