Sur les fonctions arithmétiques multiplicatives
Sur un problème de Rényi et Ivić concernant les fonctions de diviseurs de Piltz
Let Ω(n) and ω(n) denote the number of distinct prime factors of the positive integer n, counted respectively with and without multiplicity. Let denote the Piltz function (which counts the number of ways of writing n as a product of k factors). We obtain a precise estimate of the sum for a class of multiplicative functions f, including in particular , unconditionally if 1 ≤ k ≤ 3, and under some reasonable assumptions if k ≥ 4. The result also applies to f(n) = φ(n)/n (where φ is the totient...
The Continuity of the Limiting Distribution of a Function of Two Additive Functions.
The distribution of additive functions defined on short intervals
The Erdhős-Kac Theorem for Curvatures in Integral Apollonian Circle Packings
The Erdős Theorem and the Halberstam Theorem in function fields
The joint distribution of additive and complex-valued multiplicative functions
In the paper the necessary and sufficient conditions for the existence of joint limit distribution for real additive and complex-valued multiplicative function are presented.
The joint distribution of q-additive functions
The number of solutions of .
The number of unsieved integers up to x
The sum of digits of
Über additive zahlentheoretische Funktionen.
Une remarque sur les extensions pondérées de l'inégalité de Turán-Kubilius
Weighted Erdős-Kac type theorem over quadratic field in short intervals
Let be a quadratic field over the rational field and be the number of nonzero integral ideals with norm . We establish Erdős-Kac type theorems weighted by and of quadratic field in short intervals with . We also get asymptotic formulae for the average behavior of and in short intervals.