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Journal

Uniform Distribution Theory (UDT)


Volume & Issue

UDT. Volume 20. Issue 1 & 2


Published on

December, 2025


Pages

35-43


DOI

http://doi.org/10.2478/UDT-2025-0004

Article

Distribution of Leading Digits of Imaginary Parts of Riemann Zeta Zeros II


Authors

Yukio Ohkubo and Oto Strauch


Abstract

Let γn, n = 1,2, …, be the sequence of all positive imaginary parts of non-trivial zeros of the Riemann zeta function 𝜁(s) in ascending order. n this paper we give a quantitative result on the distribution of leading block of digits of γn, n = 1,2, …. For Ni =# {n ≥ 1: γn < 10i}(≥ 2) and an r-digits number D = d1d2 ··· dr, we show that the frequency.

#{ n≤Ni:(leading block of r digits of γn )=D }Ni

is approximated by

19⋅10r-1+log1018π10r-1((D+1)log10(D+1)-Dlog10D-r-19)10i-10Ni

with the explicit error bound

0.516i2Ni+1.112ilogiNi+10.452iNi+1.668logiNi-1.4741Ni.


Citation

Ohkubo, Y. & Strauch, O. (2025). Distribution of Leading Digits of Imaginary Parts of Riemann Zeta Zeros II. Uniform distribution theory, 20(1), 35-43. https://doi.org/10.2478/udt-2025-0004