Multiplicative functions and small divisors, II

K. Alladi, P. Erdős, J. D. Vaaler

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

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
Volume31
Issue number2
DOIs
Publication statusPublished - 1989

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Small Divisors
Multiplicative Functions
Divides
Square free
Number theory
Tend
Zero

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Multiplicative functions and small divisors, II. / Alladi, K.; Erdős, P.; Vaaler, J. D.

In: Journal of Number Theory, Vol. 31, No. 2, 1989, p. 183-190.

Research output: Contribution to journalArticle

Alladi, K. ; Erdős, P. ; Vaaler, J. D. / Multiplicative functions and small divisors, II. In: Journal of Number Theory. 1989 ; Vol. 31, No. 2. pp. 183-190.
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