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Acta Arithmetica

Acta Arithmetica

### A Mean-Value Theorem for Multiplicative Functions.

Mathematische Zeitschrift

### A new class of infinite products, and Euler's totient.

International Journal of Mathematics and Mathematical Sciences

Acta Arithmetica

Acta Arithmetica

Acta Arithmetica

Acta Arithmetica

Acta Arithmetica

Acta Arithmetica

### Almost-even functions as solutions of a linear functional equation

Mathematica Slovaca

### An almost-sure estimate for the mean of generalized $Q$-multiplicative functions of modulus $1$

Journal de théorie des nombres de Bordeaux

Let $Q={\left({Q}_{k}\right)}_{k\ge 0},{Q}_{0}=1,{Q}_{k+1}={q}_{k}{Q}_{k},{q}_{k}\ge 2$, be a Cantor scale, ${𝐙}_{Q}$ the compact projective limit group of the groups $𝐙/{Q}_{k}𝐙$, identified to ${\prod }_{0\le j\le k-1}𝐙/{q}_{j}𝐙$, and let $\mu$ be its normalized Haar measure. To an element $x=\left\{{a}_{0},{a}_{1},{a}_{2},\cdots \right\},0\le {a}_{k}\le {q}_{k+1}-1$, of ${𝐙}_{Q}$ we associate the sequence of integral valued random variables ${x}_{k}={\sum }_{0\le j\le k}{a}_{j}{Q}_{j}$. The main result of this article is that, given a complex $𝐐$-multiplicative function $g$ of modulus $1$, we have$\underset{{x}_{k}\to x}{lim}\left(\frac{1}{{x}_{k}}\sum _{n\le {x}_{k}-1}g\left(n\right)-\prod _{0\le j\le k}\frac{1}{{q}_{j}}\sum _{0\le a\le {q}_{j}}g\left(a{Q}_{j}\right)\right)=0\phantom{\rule{1.0em}{0ex}}\mu \text{-a.e}.$

### An application of Banach algebra techniques for multiplicative functions.

Mathematische Zeitschrift

### An Asymptotic Formula for the Variance of an Additive Function.

Mathematische Zeitschrift

Acta Arithmetica

### Application de la théorie des algèbres de mesures à l'étude des mesures spectrales.

Seminaire de Théorie des Nombres de Bordeaux

Acta Arithmetica

### Arithmetic progressions, prime numbers, and squarefree integers

Czechoslovak Mathematical Journal

In this paper we establish the distribution of prime numbers in a given arithmetic progression $p\equiv l\phantom{\rule{4.44443pt}{0ex}}\left(mod\phantom{\rule{0.277778em}{0ex}}k\right)$ for which $ap+b$ is squarefree.

### Aus der Theorie der zahlentheoretischen Funktionen.

Jahresbericht der Deutschen Mathematiker-Vereinigung

### Bemerkungen über Zulässigkeitsmengen vollständig additiver Funktionen.

Elemente der Mathematik

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