G. Kapetanakis

activity

20242026

collaborators

10 papers

math.NT2026

An estimate for incomplete mixed character sums and applications

Arpan Chandra Mazumder, Giorgos Kapetanakis, Sushant Kala +1

Let $q$ be a prime power and $m > 1$ be any integer. Let $F_{q^{m}}$ be the finite field of order $q^{m}$ and $I^¸ \in F_{q^{m}}$ be such that $\mathbb F_{q^m} = \mathbb F(Î¸)…

math.NT2025

Translates of completely normal elements and the Morgan-Mullen conjecture

Theodoulos Garefalakis, Giorgos Kapetanakis

Denote by $F_{q}$ the finite field of order $q$ and by $F_{q^{n}}$ its extension of degree $n$ . Some $a \in F_{q^{n}}$ is called primitive if it generates the multi…

math.NT2025

Normal and primitive normal elements with prescribed traces in intermediate extensions of finite fields

Arpan Chandra Mazumder, Giorgos Kapetanakis, Dhiren Kumar Basnet

In this article, we study the existence and distribution of elements in finite field extensions with prescribed traces in several intermediate extensions that are also either norma…

math.NT2025

An inductive proof of the Frobenius coin problem of two denominations

Giorgos Kapetanakis, Ioannis Rizos

Let $a, b$ be positive, relatively prime, integers. We prove, using induction, that for every $d > ab - a - b$ there exist $x, y \in Z_{\geq 0}$ , such that $d = a x + b y$ . As a byprodu…

math.NT2025

Existence of primitive normal pairs over finite fields with prescribed subtrace

K. Chatterjee, G. Kapetanakis, H. Sharma +1

Given positive integers $q, n, m$ and $a \in F_{q}$ , where $q$ is an odd prime power and $n \geq 5$ , we investigate the existence of a primitive normal pair $(I^µ, f (I^µ))$ in $\m…

math.NT2025

Normal points on Artin-Schreier curves over finite fields

Giorgos Kapetanakis, Lucas Reis

In 2022, S.D. Cohen and the two authors introduced and studied the concept of $(r, n)$ -freeness on finite cyclic groups $G$ for suitable integers $r, n$ , which is an arithmetic way…