
TL;DR
This paper investigates bounds on the size of sumsets involving dilates of a finite set of integers, providing new lower bounds and extending previous results in additive combinatorics.
Contribution
It establishes a new lower bound for the sumset involving two dilates, generalizing prior bounds and applying to large sets with specific size conditions.
Findings
Derived a new lower bound for |2A + kA| when |A| > 8k^k
Extended known bounds to more general sumsets involving dilates
Identified cases where the bound is tight, such as arithmetic progressions
Abstract
Let be a finite nonempty set of integers. An asymptotic estimate of several dilates sum size was obtained by Bukh. The unique known exact bound concerns the sum where is a prime and is large. In its full generality, this bound is due to Cilleruelo, Serra and the first author. Let be an odd prime and assume that A corollary to our main result states that Notice that if is an arithmetic progression.
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Taxonomy
TopicsAdvanced Mathematical Identities · Approximation Theory and Sequence Spaces
