科研之友
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摘要
Let f : N -> N-0 be a multiplicative arithmetic function such that for all primes p and positive integers alpha, f(p(alpha)) < p(alpha) and f(p)vertical bar f(p(alpha)). Suppose also that any prime that divides f(p(alpha)) also divides pf(p). Define f(0) = 0, and let H(n) = lim(m ->infinity) f(m)(n), where f(m) denotes the mth iterate of f. We prove that the function H is completely multiplicative.
- 出版日期2015
