Primes from sums of two squares and missing digits

Abstract

Let ${\mathcal{A}}^{\prime }$ be the set of integers missing any three fixed digits from their decimal expansion. We produce primes in a thin sequence by proving an asymptotic formula for counting primes of the form $p=m^2+{\ell }^2$, with $\ell \in {\mathcal{A}}^{\prime }$. The proof draws on ideas from the work of Friedlander-Iwaniec on primes of the form $p=x^2+y^4$, as well as ideas from the work of Maynard on primes with restricted digits.

60 pages