Hall 123

On a sumset problem for dilated integer sets

Jagannath Bhanja

IMSc, Chennai

Let $A$ be a non-empty finite set of integers. For any integer $k$, let $A+k\cdot A=\{a_1+ka_2: a_1,a_2\in A\}$. In 2010, Cilleruelo, Silva, and Vinuesa conjectured that, if $k$ is a positive integer and $A$ is a finite set of integers with sufficiently large cardinality, then the sumset $A+k\cdot A$ contains at least $(k+1)|A|-\lceil k(k+2)/4\rceil$ number of distinct elements. For some values of $k$, this conjecture is already confirmed. In this talk, I shall discuss one of our recent works in which we confirmed some cases of this conjecture under certain restrictions on set $A$.