Sums and Products with Smooth Numbers
William D. Banks, David Covert
TL;DR
This paper investigates the sizes of sumsets and productsets for smooth numbers, providing estimates for the sets formed by sums and products of integers with restricted prime factors.
Contribution
It offers new estimates for sumsets and productsets specifically for smooth numbers, a class of integers with prime factors below a certain threshold.
Findings
Estimated sizes of A + A for smooth numbers.
Estimated sizes of A · A for smooth numbers.
Provided bounds for sumset and productset sizes.
Abstract
We estimate the sizes of the sumset A + A and the productset A A in the special case that A = S (x, y), the set of positive integers n less than or equal to x, free of prime factors exceeding y.
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Taxonomy
TopicsAnalytic Number Theory Research · Limits and Structures in Graph Theory · Graph Labeling and Dimension Problems