G. Shakan

activity

20052022

most citedOn higher energy decompositions and the sum-product phenomenon

29 citations · 64 across the 16 of their papers we have counts for

collaborators

Showing 2014Show all

2 papers · 1 filter

math.NT2014★ 2 cited

Sum of dilates in vector spaces

Antal Balog, George Shakan

Let $d \geq 2$ , $A \subset Z^{d}$ be finite and not contained in a translate of any hyperplane, and $q \in Z$ such that $∣ q ∣ > 1$ . We show $$|A+ q \cdot A| \geq (|q|…

math.NT2014★ 4 cited

Sum of many dilates

George Shakan

We show that for any coprime integers $λ_{1}, \dots, λ_{k}$ and any finite $A \subset Z$ , one has $$|λ_1 \cdot A + \ldots + λ_k \cdot A| \geq (|λ_1| + \ldots + |λ_k|)|A|- C…