(i) Additive Arithmetic Functions Bounded by Monotone Functions on Thin Sets
نویسنده
چکیده
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 such integers which do not exceed x . THEOREM 1 . Let the additive arithmetic function f(n) satisfy
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