Additive decomposability of multiplicatively defined sets

Christian Elsholtz*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    Abstract

    Let Q (T) denote the set of integers which are composed of prime factors from a given set of primes T only. Suppose that A+BQ′(T), where Q(T) and Q′(T) difier at flnitely many elements only. Also assume that τ log x+O(1). We prove that A(N)B(N) = O(N(log N)) holds. In the case we give an example where both A(N) and B(N) are of order of magnitude which shows that this is close to best possible.

    Original languageEnglish
    Pages (from-to)61-77
    Number of pages17
    JournalFunctiones et Approximatio, Commentarii Mathematici
    Volume35
    DOIs
    Publication statusPublished - 1 Jan 2006

    Keywords

    • Additive decompositions of sets
    • Inverse Goldbach problem
    • Sums of two squares

    ASJC Scopus subject areas

    • Mathematics(all)

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