Avnish K. Sharma

activity

20212026

collaborators

4 papers

math.NT2026

Primitive Polynomials of the Form $g (x) + λ$ over Finite Fields: Non-Existence Results and Conjectures

Avnish K. Sharma

In this paper, we investigate the existence of primitive polynomials over $F_{q^{n}}$ whose constant term is a primitive element of $F_{q^{n}}$ . We prove that such po…

math.NT2024

On $r$ -primitive $k$ -normal polynomials with two prescribed coefficients

Avnish K. Sharma, Mamta Rani, Sharwan K. Tiwari +1

This article investigates the existence of an $r$ -primitive $k$ -normal polynomial, defined as the minimal polynomial of an $r$ -primitive $k$ -normal element in $F_{q^{n}}$ , w…

math.NT2022

Inverses of $r$ -primitive $k$ -normal elements over finite fields

Mamta Rani, Avnish K. Sharma, Sharwan K. Tiwari +1

Let $r$ , $n$ be positive integers, $k$ be a non-negative integer and $q$ be any prime power such that $r ∣ q^{n} - 1.$ An element $α$ of the finite field $F_{q^{n}}$ is called…

math.NT2021

Primitive Normal Values of Rational Functions over Finite Fields

Avnish K. Sharma, Mamta Rani, Sharwan K. Tiwari

In this paper, we consider rational functions $f$ with some minor restrictions over the finite field $F_{q^{n}},$ where $q = p^{k}$ for some prime $p$ and positive integer $k$ .…

Primitive Polynomials of the Form g(x)+λ over Finite Fields: Non-Existence Results and Conjectures

On r-primitive k-normal polynomials with two prescribed coefficients

Inverses of r-primitive k-normal elements over finite fields

Primitive Normal Values of Rational Functions over Finite Fields

Primitive Polynomials of the Form $g (x) + λ$ over Finite Fields: Non-Existence Results and Conjectures

On $r$ -primitive $k$ -normal polynomials with two prescribed coefficients

Inverses of $r$ -primitive $k$ -normal elements over finite fields