On primes represented by quartic polynomials on average

2019/08/26 by Kam Hung Yau, Yau, Kam Hung
Mathematics · #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1908.09439

openalex publication_date 2019/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain an upper bound for the distribution of primes in the form n⁴ + k up to x, averaged over k with small square-full part. As a corollary, we show that for almost all k, there is an expected amount of primes in the form n⁴ +k up to x.

Related

• On primes of the form n₁^u + n₂^v + k, on average
• Primes values of a² + p⁴
• Primes in arithmetic progressions on average II
• On the distribution of αp²+β modulo one for primes p such that p+2 has no more two prime divisors
• On primes in arithmetic progressions and bounded gaps between many primes