Prime Values of Quadratic Polynomials

Abstract

This note investigates the prime values of the polynomial $f(t)=q{t}^2+a$ for any fixed pair of relatively prime integers $a\ge 1$ and $q\ge 1$ of opposite parity. For a large number $x\ge 1$, an asymptotic result of the form ${\sum }_{n\le x^{1/2},n\text{ odd}}\Lambda (q{n}^2+a)\gg q{x}^{1/2}/2\phi (q)$ is achieved for $q\ll (\log x{)}^b$, where $b\ge 0$ is a constant.

Ten Pages. Keywords: Distribution of Primes; Polynomial Prime Values; Bateman-Horn Conjecture

References in corpus (1)

• Some experiments on Bateman-Horn