Popular differences in primes along fractional powers

Bora Çalım, Ioannis Iakovakis, Sophie Long +2

We prove that ${\mathbb{E}}_{m\le M}{\mathbb{E}}_{n\le N}\Lambda (n)\Lambda (n+\lfloor m^c\rfloor )=1+\mathrm{O}({\log }^{2-\mathrm{Bc}}\mathrm{N})$, where $c>2$ is a non-intege…