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### A characterization of some additive arithmetical functions, III

Acta Arithmetica

I. Introduction. In 1946, P. Erdős [2] proved that if a real-valued additive arithmetical function f satisfies the condition: f(n+1) - f(n) → 0, n → ∞, then there exists a constant C such that f(n) = C log n for all n in ℕ*. Later, I. Kátai [3,4] was led to conjecture that it was possible to determine additive arithmetical functions f and g satisfying the condition: there exist a real number l, a, c in ℕ*, and integers b, d such that f(an+b) - g(cn+d) → l, n → ∞. This problem has been treated...

Acta Arithmetica

Acta Arithmetica

Acta Arithmetica

### A note on the parity of the sum-of-digits function.

Séminaire Lotharingien de Combinatoire [electronic only]

Acta Arithmetica

### A Remark on a Certain Class of Arithmetic Functions

Publications de l'Institut Mathématique

Acta Arithmetica

Acta Arithmetica

### Abundant numbers and the Riemann hypothesis.

Experimental Mathematics

### An example for Gelfand's theory of commutative Banach algebras

Mathematica Slovaca

### Arithmetic properties of positive integers with fixed digit sum.

Revista Matemática Iberoamericana

In this paper, we look at various arithmetic properties of the set of those positive integers n whose sum of digits in a fixed base b &gt; 1 is a fixed positive integer s. For example, we prove that such integers can have many prime factors, that they are not very smooth, and that most such integers have a large prime factor dividing the value of their Euler φ function.

### Arithmetical properties of finite rings and algebras, and analytic number theory. VI. Maximum Orders of Magnitude.

Journal für die reine und angewandte Mathematik

Acta Arithmetica

### Calculating a determinant associated with multiplicative functions

Bollettino dell'Unione Matematica Italiana

Let $h$ be a complex valued multiplicative function. For any $N\in \mathbb{N}$, we compute the value of the determinant ${D}_{N}:={det}_{i|N,j|N}\left(\frac{h\left(\left(i,j\right)\right)}{ij}\right)$ where $\left(i,j\right)$ denotes the greatest common divisor of $i$ and $j$, which appear in increasing order in rows and columns. Precisely we prove that ${D}_{N}=\prod _{p{}^{l}\parallel N}{\left(\frac{1}{{p}^{l\left(l+1\right)}}\stackrel{l}{\prod _{i=1}}\left(h\left({p}^{i}\right)-h\left({p}^{i-1}\right)\right)\right)}^{\tau \left(N/{p}^{l}\right)}.$ This means that ${D}_{N}^{1/\tau \left(N\right)}$ is a multiplicative function of $N$. The algebraic apparatus associated with this result allows us to prove the following two results. The first one is the characterization of real multiplicative functions $f\left(n\right)$, with $0\le f\left(p\right)<1$, as minimal values of certain...

Acta Arithmetica

Acta Arithmetica

Acta Arithmetica

Acta Arithmetica

### Die Ramanujan-Entwicklung reellwertiger multiplikativer Funktionen vom Betrage kleiner oder gleich Eins.

Journal für die reine und angewandte Mathematik

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