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Let $Q = {(Q_{k})}_{k \geq 0}, Q_{0} = 1, Q_{k + 1} = q_{k} Q_{k}, q_{k} \geq 2$ , be a Cantor scale, $𝐙_{Q}$ the compact projective limit group of the groups $𝐙 / Q_{k} 𝐙$ , identified to $\prod_{0 \leq j \leq k - 1} 𝐙 / q_{j} 𝐙$ , and let $μ$ be its normalized Haar measure. To an element $x = {a_{0}, a_{1}, a_{2}, \dots}, 0 \leq a_{k} \leq q_{k + 1} - 1$ , of $𝐙_{Q}$ we associate the sequence of integral valued random variables $x_{k} = \sum_{0 \leq j \leq k} a_{j} Q_{j}$ . The main result of this article is that, given a complex $𝐐$ -multiplicative function $g$ of modulus $1$ , we have $lim_{x_{k} \to x} (\frac{1}{x_{k}} \sum_{n \leq x_{k} - 1} g (n) - \prod_{0 \leq j \leq k} \frac{1}{q_{j}} \sum_{0 \leq a \leq q_{j}} g (a Q_{j})) = 0 μ -a.e .$

In this paper we establish the distribution of prime numbers in a given arithmetic progression $p \equiv l (m o d k)$ for which $a p + b$ is squarefree.

Aus der Theorie der zahlentheoretischen Funktionen.

Wolfgang Schwarz (1976/1977)

Jahresbericht der Deutschen Mathematiker-Vereinigung

Bemerkungen über Zulässigkeitsmengen vollständig additiver Funktionen.

Thomas Jahnke (1981)

Elemente der Mathematik

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Displaying 1 – 20 of 173

A conjecture of Kátai

A local Turán-Kubilius inequality

A Mean-Value Theorem for Multiplicative Functions.

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

A stopping time problem on the positive integers

A Turán-Kubilius type inequality on sum sets

Absolutely continuous distribution functions of additive functions $f (p) = {(l o g p)}^{- a}, a > 0$

Additive functions monotonic on the set of primes

Additive functions with respect to expansions over the set of Gaussian integers

Additive functions with restricted growth on the numbers of the form p+1

Almost-even functions as solutions of a linear functional equation

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

An application of Banach algebra techniques for multiplicative functions.

An Asymptotic Formula for the Variance of an Additive Function.

An Erdös-Kac theorem for integers without large prime factors

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

Arithmetic functions on Beatty sequences

Arithmetic progressions, prime numbers, and squarefree integers

Aus der Theorie der zahlentheoretischen Funktionen.

Bemerkungen über Zulässigkeitsmengen vollständig additiver Funktionen.

Currently displaying 1 – 20 of 173