Average growth-behavior and distribution properties of generalized weighted digit-block-counting functions |
| |
Authors: | Roswitha Hofer Gerhard Larcher Friedrich Pillichshammer |
| |
Affiliation: | (3) Department of Mathematics and Computer Science, Babeş-Bolyai University of Cluj, Cluj-Napoca, Romania;(4) formerly the Technical University of Timişoara, Timişoara, Romania; |
| |
Abstract: | We introduce a generalized weighted digit-block-counting function on the nonnegative integers, which is a generalization of many digit-depending functions as, for example, the well known sum-of-digits function. A formula for the first moment of the sum-of-digits function has been given by Delange in 1972. In the first part of this paper we provide a compact formula for the first moment of the generalized weighted digit-block-counting function and show that a (weak) Delange type formula holds if the sequence of weights converges. The question, whether the converse is true as well, can only be answered partially at the moment. In the second part of this paper we study distribution properties of generalized weighted digit-block-counting sequences and their d-dimensional analogues. We give an if and only if condition under which such sequences are uniformly distributed modulo one. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|