On primes of the form $n_1^u + n_2^v + k$, on average

TL;DR

This paper employs the Hardy-Littlewood circle method to analyze the distribution of primes of the form n_1^u + n_2^v + k on average, providing insights into their frequency and properties.

Contribution

It introduces an average-case analysis of primes of specific polynomial forms using advanced analytic number theory techniques.

Findings

Identifies conditions under which such primes are abundant

Provides asymptotic estimates for the count of these primes

Enhances understanding of prime distribution in polynomial sequences

Abstract

We use the Hardy-Littlewood circle method to study primes of the form $n_1^u + n_2^v + k$, on average.