DISTRIBUTION FUNCTIONS OF ADDITIVE ARITHMETIC FUNCTIONS

Functional Analysis and Additive Arithmetic Functions

1. A function is arithmetic if it is defined on the positive integers. Those arithmetic functions which assume real values and satisfy f(ab)-f(a)+f(b) for mutually prime integers a, b are classically called additive. The following examples illustrate the interest of these functions, both for themselves and for their applications. An additive function is defined by its values on the prime powers...

THE JOINT DISTRIBUTION OF q-ADDITIVE FUNCTIONS

q-ADDITIVE FUNCTIONS AND WELL DISTRIBUTION

Approximately generalized additive functions in several variables

The goal of  this paper is to investigate the solutionand stability in random normed spaces, in non--Archimedean spacesand also in $p$--Banach spaces and finally the stability using thealternative fixed point of generalized additive functions inseveral variables.

(i) Additive Arithmetic Functions Bounded by Monotone Functions on Thin Sets

1 . An arithmetic function f(n) is said to be additive if it satisfies the relation f(ob) = f(a)+f(b) for every pair of coprime positive integers a, b . In this paper we establish two results to the effect that an additive function which is not too large on many integers cannot often be large on the primes . If a l <a,< . . . is a sequence of positive integers, let A(x) denote ttie number of su...