Uniform Distribution Theory 14(1), pp. 19-42.
ISSN/ISBN: Not available at this time. DOI: 10.2478/udt-2019–0003
Abstract: In this paper, we study the sequence (f(pn))n≥1, where pn is the nth prime number and f is a function of a class of slowly increasing functions including f(x) = logb xr and f(x) = logb(xlogx)r, where b ≥ 2 is an integer and r > 0 is a real number. We give upper bounds of the discrepancy DN∗ (f(pn), g) for a distribution function g and a sub-sequence (Ni)i≥1 of the natural numbers. Especially for f(x) = logb xr, we obtain the effective results for an upper bound of DN∗i(f(pn),g).
Bibtex:
@article{,
author = {Yukio Ohkubo and Oto Strauch},
title = {Distribution of Leading Digits of Numbers II},
year = {2019},
journal = {Uniform Distribution Theory},
volume = {14},
number = {1},
pages = {19--42},
doi = {10.2478/udt-2019–0003},
}
Reference Type: Journal Article
Subject Area(s): Analysis, Number Theory