Cubic congruences and binary quadratic forms
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915222102474752 |
|---|---|
| author | Sun, Zhi-Hong |
| author_facet | Sun, Zhi-Hong |
| contents | Let $p>3$ be a prime, $a_1,a_2,a_3\in\Bbb Z$ and let $N_p(x^3+a_1x^2+a_2x+a_3)$ denote the number of solutions to the congruence $x^3+a_1x^2+a_2x+a_3\equiv 0\pmod p$. In this paper, we give an explicit criterion for $N_p(x^3+a_1x^2+a_2x+a_3)=3$ via binary quadratic forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12861 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cubic congruences and binary quadratic forms Sun, Zhi-Hong Number Theory Primary 11A07, Secondary 11A15, 11B37, 11B39, 11E16 Let $p>3$ be a prime, $a_1,a_2,a_3\in\Bbb Z$ and let $N_p(x^3+a_1x^2+a_2x+a_3)$ denote the number of solutions to the congruence $x^3+a_1x^2+a_2x+a_3\equiv 0\pmod p$. In this paper, we give an explicit criterion for $N_p(x^3+a_1x^2+a_2x+a_3)=3$ via binary quadratic forms. |
| title | Cubic congruences and binary quadratic forms |
| topic | Number Theory Primary 11A07, Secondary 11A15, 11B37, 11B39, 11E16 |
| url | https://arxiv.org/abs/2503.12861 |