Andrew Lott: Sárközy's theorem in $\mathbb{F}_q[t]$ via the van der Corput property

Fix a positive prime power $q$, and  let $\F$ be the ring of polynomials over the finite field $\mathbb{F}_q$. Suppose $A \subseteq \{f \in \F : \deg f \leq N\}$ contains no pair of elements whose difference is of the form $P-1$ with $P$ irreducible. Adapting Green's approach to Sárközy's theorem for shifted primes in $\Z$ using the van der Corput property, we show that \[
|A| \ll q^{(N+1)(11/12+o(1))},
\] improving upon the bound $O\big(q^{(1-c/\log N)(N+1)}\big)$ due to L\^{e} and Spencer.

Joint work with Steve Fan
 

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