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arXiv · 2111.04136

Prime values of $f(a,b^2)$ and $f(a,p^2)$, $f$ quadratic

Stanley Yao Xiao
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Abstract

We prove an asymptotic formula for primes of the shape $f(a,b^2)$ with $a,b$ integers and of the shape $f(a,p^2)$ with $p$ prime. Here $f$ is a binary quadratic form with integer coefficients, irreducible over $\mathbb{Q}$ and has no local obstructions. This refines the seminal work of Friedlander and Iwaniec on primes of the form $x^2 + y^4$ and Heath-Brown and Li on primes of the form $a^2 + p^4$, as well as earlier work of the author with Lam and Schindler on primes of the form $f(a,p)$ with $f$ a positive definite form.

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Stanley Yao Xiao. 2021-11-07. Prime values of $f(a,b^2)$ and $f(a,p^2)$, $f$ quadratic. https://doi.org/10.2140/ant.2024.18.1619

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