An explicit power-saving bound for S\'{a}rk\"{o}zy's Theorem on shifted primes, assuming GRH

Abstract

Assume the Generalised Riemann Hypothesis. If $A\subseteq \{1,...,N\}$ contains no two elements differing by $p+1$, $p$ prime, then $|A|\ll N^{\frac{89}{90} + o(1)}$.