Author

D. Ghioca

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Preprint Oct 2026

Covering plane curves over finite fields with lines

We prove that, for every fixed $d\geq 2$ and $\varepsilon>0$, the $\mathbb{F}_q$-points of a geometrically irreducible reflexive plane curve of degree $d$ over $\mathbb{F}_q$ can be covered by at most $\left(\frac{1}{d}+\varepsilon\right)q$ many $\mathbb{F}_q$-lines, provided that $q$ is sufficiently large. The same co...

Shamil Asgarli, Sarthak Dassarma, D. Ghioca et al. · 0 citations

Preprint Jul 2026

Collision of Orbits for Families of Polynomials Defined over Number Fields

Let $d\ge 2$ be an integer and let $c_0(t),\dots, c_{d-2}(t)\in\bar{\mathbb{Q}}[t]$. We consider the family of normalized polynomials $f_\lambda(z):=z^d+\sum_{i=0}^{d-2} c_i(\lambda)\cdot z^i$ parameterized by $\lambda\in\bar{\mathbb{Q}}$; the generic element of our family of polynomials is $f_t(z):=z^d+\sum_{i=0}^{d-2...

D. Ghioca, Negin Shadgar · 0 citations