Abstract

Letf(m) be a real-valued, number theoretic function . We say thatf(m) is additive if f(mn) = f(m) +f(n) whenever (m, n) = 1 . If f(m) satisfies the additional restriction that f(p) = f(p2) _ f(p3) = . . ., then we say that f(m) is strongly additive . We denote the class of additive functions by .4. A function fEF .2/ is called finitely monotonic if there exists an infinite sequence xk -+ oo and a positive constant A, so that for each xk there are integers

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