H. Sharma

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20192026

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6 papers · 1 filter

math.NT2024

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 $(ε, f (ε))$ in $\mat…

math.NT2024

Arithmetic progression in a finite field with prescribed norms

Kaustav Chatterjee, Hariom Sharma, Aastha Shukla +1

Given a prime power $q$ and a positive integer $n$ , let $F_{q^{n}}$ represents a finite extension of degree $n$ of the finite field $F_{q}$ . In this article, we…

math.NT2023

A primitive normal pair in a finite field with prescribed traces and norms

Kaustav Chatterjee, Hariom Sharma, Shailesh Kumar Tiwari

Given $F_{p^{t}}$ , a field with $p^{t}$ elements, where $p$ is a prime power, $t$ is a positive integer. Let $f (x)$ be a polynomial over $F_{p^{t}}$ of degree $m$ wit…

math.NT2021

Existence of Primitive Normal Pairs with One Prescribed Trace over Finite Fields

Hariom Sharma, R. K. Sharma

Given $m, n, q \in N$ such that $q$ is a prime power and $m \geq 3$ , $a \in F_{q}$ , we establish a sufficient condition for the existence of primitive pair $(α, f (α))$ …

math.NT2020

Existence of Primitive Pairs with Prescribed Traces over Finite Fields

Hariom Sharma, R. K. Sharma

Let $F = F_{q^{m}}$ , $m > 6$ , $n$ a positive integer, and $f = p / q$ with $p$ , $q$ co-prime irreducible polynomials in $F [x]$ and deg $(p)$ $+$ deg $(q) = n$ . A sufficient condition h…

math.NT2019

Primitive values of rational functions at primitive elements of a finite field

Stephen D. Cohen, Hariom Sharma, Rajendra Sharma

Given a prime power $q$ and an integer $n \geq 2$ , we establish a sufficient condition for the existence of a primitive pair $(α, f (α))$ where $α \in F_{q}$ and $f(x) \in \mathb…