Primes values of a² + p⁴

2015/04/02 by D. R. Heath‐Brown, Heath-Brown, D. R., Xiannan Li +1
Mathematics · #11P32 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1504.00531

openalex publication_date 2015/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove an asymptotic formula for the number of primes of the shape a² +p⁴, 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 x².

Citations

• Primes represented by x3+2y3

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