On the distribution of arithmetic functions.

      Аннотация: This book deals with the distribution of arithmetic functions under digital constraint and related questions. The word "distribution" refers to various concepts and facts, including uniform distribution and distribution functions of certain sequences. Indeed, we study the distribution of the largest prime factor of an integer with restriction to strongly q-additive functions. Next, we are interested in a k-freeness problem. Then, we consider the distribution of additive functions subject to certain congruence conditions. Particularly, we prove an Erdos-Kac type theorem for primes verifying a digital constraint.

Ключевые слова: Digital function, Exponential sum, k-free numbers, largest prime factor, sum of digits function, uniform distribution modulo 1