Problems and results on additive properties of general sequences. I

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Abstract

Let a1 <a2 <… be an infinite sequence of positive integers and denote by R(n) the number of solutions of n = ai + aj. The authors prove that if F(n) is a monotonic increasing arithmetic function with F(n) → +∞ and F(n) = o(n(log n)-2) then |R(n) - F(n)| = o((F(n))1/2) cannot hold.

Original languageEnglish
Pages (from-to)347-357
Number of pages11
JournalPacific Journal of Mathematics
Volume118
Issue number2
Publication statusPublished - 1985

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ASJC Scopus subject areas

  • Mathematics(all)

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