2003/11/13 by Ernie Croot, Croot, Ernie
Mathematics · #11N25 #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.CO #math.NT #msc:11N25
paper · pdf · doi:10.48550/arxiv.math/0311226
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openalex publication_date 2003/11/13 · arxiv created 2003/11/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we present a method for producing asymptotic estimates for the number of integers in a given S having only ``small'' prime factors. The conditions that need to be verified are simpler than those required by other methods, and we apply our result to give an easy proof of a result which says that dense subsets A and B of 1,2,...,x always produce asymptotically the expected number of xr - smooth sums a+b, where a in A and b in B. Recall that a number n is said to be y-smooth if all its prime divisors are at most y.