Primes values of $a^2 + p^4$

TL;DR

This paper establishes an asymptotic count for primes of the form a^2 + p^4, refining previous results, and demonstrates prime equidistribution in large moduli up to nearly x^2.

Contribution

It provides a new asymptotic formula for primes of the form a^2 + p^4 and advances understanding of prime distribution in large moduli.

Findings

Asymptotic formula for primes of the form a^2 + p^4

Prime equidistribution in moduli up to nearly x^2

Refinement of Friedlander and Iwaniec's work

Abstract

We prove an asymptotic formula for the number of primes of the shape $a^2 +p^4$, thereby refining the well known work of Friedlander and Iwaniec. Along the way, we prove a result on equidistribution of primes up to $x$, in which the moduli may be almost as large as $x^2$.