Saeed Tafazolian

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math.NT2026

Maximal and minimal curves of the form $y^{3} = x^{(q^{2} + 1) /2} + x$

Guilherme Dias, Saeed Tafazolian

Let $p \geq 5$ be a prime with $p \equiv - 1 (mod 3)$ , let $q = p^{r}$ , and consider \[ \cC:\qquad y^3=x^{(q^2+1)/2}+x \] over $\F_{q^6}$. We prove the exact formula \[ \#\cC(\F_{q^6})=q^6+…

math.NT2025

CM theory, maximal hyperelliptic curves, and Chebyshev polynomials

Saeed Tafazolia, Jaap Top

This paper studies hyperelliptic curves $\cH_d$ corresponding to $y^{2} = φ_{d} (x)$ over finite fields, with $φ_{d} (x)$ a Chebyshev polynomial. Starting from the case where $d = ℓ$ is an…

Maximal and minimal curves of the form y3=x(q2+1)/2+x

CM theory, maximal hyperelliptic curves, and Chebyshev polynomials

Maximal and minimal curves of the form $y^{3} = x^{(q^{2} + 1) /2} + x$