Additive decomposability of multiplicatively defined sets

Christian Elsholtz

doi:10.7169/facm/1229442617

Additive decomposability of multiplicatively defined sets

Christian Elsholtz^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-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)^2τ) 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 language	English
Pages (from-to)	61-77
Number of pages	17
Journal	Functiones et Approximatio, Commentarii Mathematici
Volume	35
DOIs	https://doi.org/10.7169/facm/1229442617
Publication status	Published - 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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10.7169/facm/1229442617

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KW - Additive decompositions of sets

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KW - Sums of two squares

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Additive decomposability of multiplicatively defined sets

Abstract

Keywords

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