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A strong sum-product "for translates" in finite fields

In the course of some recent research, I've sketched out a proof of the following result. My basis question is: is the result interesting? Proposition There exists an absolute constant $c$ such ...
Nick Gill's user avatar
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3 votes
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Under what conditions on $A$ and $v$ is the size of the sumset $v \cdot A + A$ over $\mathbb{F}_p$ equal or close to $|A|^2$?

Let $p$ be a prime, let $A$ be a subset of $\mathbb{F}_p$, and let $v \in \mathbb{F}_p \setminus \{0\}$. Under what conditions is $|v \cdot A + A|$ (that is, $|\{ va + b : a \in A,\ b \in A \}|$) ...
Daira-Emma Hopwood's user avatar