On the asymptotics of Kempner–Irwin sums
Abstract
Let [Formula: see text] be the subseries of the harmonic series keeping the integers having exactly [Formula: see text] occurrences of the digit [Formula: see text] in base [Formula: see text]. We prove the existence of an asymptotic expansion to all orders in descending powers of [Formula: see text], for fixed [Formula: see text] and [Formula: see text], of [Formula: see text]. We explicitly give, depending on cases, either four or five terms. The coefficients involve the values of the zeta function at the integers.
Fields of Study & Subjects
Analytic Number Theory Research
Meromorphic and Entire Functions
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- International Journal of Number Theory
- Publisher
- World Scientific Pub Co Pte Ltd
- Pages
- 1–40
- Publication date
- 18 July 2026
- Language
- EN