Prime values of $f(a,b^2)$ and $f(a,p^2)$, $f$ quadratic
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866916409073729536 |
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| author | Xiao, Stanley Yao |
| author_facet | Xiao, Stanley Yao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_04136 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Prime values of $f(a,b^2)$ and $f(a,p^2)$, $f$ quadratic Xiao, Stanley Yao Number Theory 11N32 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. |
| title | Prime values of $f(a,b^2)$ and $f(a,p^2)$, $f$ quadratic |
| topic | Number Theory 11N32 |
| url | https://arxiv.org/abs/2111.04136 |