Multiplicative functions and small divisors, II

K. Alladi, P. Erdös, J. D. Vaaler

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Let n be square-free and h a multiplicative function satisfying 0 ≤ h(p) ≤ 1 (k - 1) on primes p, where k ≥ 2. It is shown that ∑ d{divides}nh(d)≤(2k+o(1)) ∑ d{divides}n,d≤n 1 kh(d) fork=2,3,4..., where o(1) is a quantity that tends to zero as Σpβn 1 = v(n) → ∞. Such inequalities have applications to Probabilistic Number Theory.

Original languageEnglish
Pages (from-to)183-190
Number of pages8
JournalJournal of Number Theory
Issue number2
Publication statusPublished - Feb 1989


ASJC Scopus subject areas

  • Algebra and Number Theory

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