Zhi-Hong Sun

activity

20232025

collaborators

3 papers

math.NT2025

Cubic congruences and binary quadratic forms

Zhi-Hong Sun

Let $p > 3$ be a prime, $a_{1}, a_{2}, a_{3} \in Z$ and let $N_{p} (x^{3} + a_{1} x^{2} + a_{2} x + a_{3})$ denote the number of solutions to the congruence $x^{3} + a_{1} x^{2} + a_{2} x + a_{3} \equiv 0 (mod p)$ . In this paper…

math.NT2024

Elliptic curves and the residue-counts of $x^{2} + b x + c / x$ modulo $p$

Zhi-Hong Sun

For any prime $p > 3$ and rational $p$ -integers $b, c$ with $c (b^{3} - 27 c) \neq \equiv 0 (mod p)$ let $V_{p} (x^{2} + b x + \frac{c}{x})$ be the residue-counts of $x^{2} + b x + \frac{c}{x}$ modulo $p$ as $x$ run…

math.NT2023

The residue-counts of $x^{2} + a / x$ modulo a prime

Zhi-Hong Sun

For a prime $p > 3$ and $a \in Z$ with $p ∤ a$ let $V_{p} (x^{2} + \frac{a}{x})$ be the residue-counts of $x^{2} + \frac{a}{x}$ modulo $p$ as $x$ runs over $1, 2, \dots, p - 1$ . In this paper, we…

Cubic congruences and binary quadratic forms

Elliptic curves and the residue-counts of x2+bx+c/x modulo p

The residue-counts of x2+a/x modulo a prime

Elliptic curves and the residue-counts of $x^{2} + b x + c / x$ modulo $p$

The residue-counts of $x^{2} + a / x$ modulo a prime