An Explicit Formula of Subblock Occurrences for the p-Adic Expansion

Katsushi MURAMOTO; Tatsuya OKADA; Takeshi SEKIGUCHI; Yasunobu SHIOTA

doi:10.4036/iis.2002.115

Interdisciplinary Information Sciences

Online ISSN : 1347-6157
Print ISSN : 1340-9050
ISSN-L : 1340-9050

An Explicit Formula of Subblock Occurrences for the p-Adic Expansion

Katsushi MURAMOTO, Tatsuya OKADA, Takeshi SEKIGUCHI, Yasunobu SHIOTA

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Keywords: digital sum problem, singular function, multinomial measure

JOURNAL FREE ACCESS

2002 Volume 8 Issue 1 Pages 115-121

DOI https://doi.org/10.4036/iis.2002.115

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Abstract

Let b(n,w) be the number of occurrences of subblock w in the p-adic expansion of n ∈ N and set B(N,w)=Σ_n=0^Nb(n,w) for N ∈ N. Properties of the value of B(N,w) were investigated by Prodinger [8] (for p=2) and by Kirschenhofer [3] (for a general p). In this paper we give a simple representation of B(N,w) by means of previous result [5] on the explicit formula of generalized power and exponential sums of digital sums.

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