Primes from sums of two squares and missing digits

TL;DR

This paper develops a method to count primes of the form p = m^2 + l^2 where l's decimal expansion omits three fixed digits, combining techniques from Friedlander-Iwaniec and Maynard to handle primes with digit restrictions.

Contribution

It provides an asymptotic formula for primes in a thin sequence with digit restrictions, extending previous methods to new prime forms.

Findings

Established an asymptotic count for primes of the form p = m^2 + l^2 with digit restrictions.

Extended techniques from Friedlander-Iwaniec and Maynard to this new setting.

Demonstrated the existence of primes missing specific digits within certain algebraic forms.

Abstract

Let $\mathcal{A}'$ 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 $\ell \in \mathcal{A}'$. 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.