Prime values of f(a,b2) and f(a,p2), f quadratic,Algebra & Number Theory

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Prime values of f(a,b2) and f(a,p2), f quadratic
Algebra & Number Theory ( IF 0.9 ) Pub Date : 2024-09-19 , DOI: 10.2140/ant.2024.18.1619
Stanley Yao Xiao

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 $ℚ$ and has no local obstructions. This refines the seminal work of Friedlander and Iwaniec on primes of the form $x^{2} + y^{4}$ and of 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.

更新日期：2024-09-19

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