Saeed Tafazolian

collaborators

5 papers

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.AG2026

Automorphisms of Plane Curves defined from Chebychev polynomials

Saeed Tafazolian, Jaap Top

We investigate the automorphism groups of the algebraic curves \[ \mathcal{C}_d : y^d = Ï_d(x), \] where $I ¨ _{d} (x)$ denotes the Chebyshev polynomial of degree $d$ , defined over a f…

math.AG2025

Explicit Families of Hyperelliptic Curves with CM Jacobians

Saeed Tafazolian, Jaap Top

We construct explicit families of hyperelliptic curves over $\QQ$ whose Jacobians admit complex multiplication (CM). Each curve in these families is defined by \[ v^2 = (u+2)\,Ï_d…

math.AG2025

Locally recoverable codes with multiple recovering sets from maximal curves

Saeed Tafazolian, Jaa Top

In this paper, we present a construction of locally recoverable codes (LRCs) with multiple recovery sets using algebraic curves with many rational points. By leveraging separable m…

math.NT2025

CM theory, maximal hyperelliptic curves, and Chebyshev polynomials

Saeed Tafazolia, Jaap Top

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

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

Automorphisms of Plane Curves defined from Chebychev polynomials

Explicit Families of Hyperelliptic Curves with CM Jacobians

Locally recoverable codes with multiple recovering sets from maximal curves

CM theory, maximal hyperelliptic curves, and Chebyshev polynomials

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