The distribution of real-valued \(Q\)-additive functions modulo 1
type: Item
instance of: scholarly article
zbMATH Open document ID: 0984.11039
author: Abigail Hoit
published in: Acta Arithmetica
publication date: 2002-02-21T00:00:00Z
full work available at URL: 100-2-2.html
Mathematics Subject Classification ID: 11K16
zbMATH DE Number: 1709877
zbMATH Keywords: distribution mod 1
zbMATH Keywords: \(q\)-additive functions
zbMATH Keywords: \(q\)-multiplicative functions
MaRDI profile type: Publication
OpenAlex ID: W2084375226
DOI: 10.4064/AA100-2-2
title: The distribution of real-valued \(Q\)-additive functions modulo 1
review text: A mixed radix system \(Q=\{Q_j\}_{j\geq 0}\) is a sequence of strictly increasing positive integers \(Q_j\) with \(Q_0=1\) such that \(Q_j|Q_{j+1}\) for all \(j\). Then each non-negative integer \(n\) has a unique representation \(n=\sum_{j\geq 0}a_j(n)Q_j\), and a \(Q\)-additive function is of the form \(f(n)=\sum_{j\geq 0}f_j(a_j(n))\) where \(f_j(0)=0\). A simple example of a \(Q\)-additive function is the sum-of-digits function. The author investigates conditions under which the sequence \((f(n))\) has a limit distribution mod 1. In order to prove this result, the author considers so-called \(Q\)-multiplicative functions and establishes mean value theorems for these.
reviewed by: Peter Schatte
description: scientific article; zbMATH DE number 1709877