Arithmetic progression in a finite field with prescribed norms

2024/01/03 by Chatterjee, Kaustav, Sharma, Hariom, Shukla, Aastha +1
#11T23 #12E20 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2401.01819

Abstract

Given a prime power q and a positive integer n, let \mathbbF_qⁿ represents a finite extension of degree n of the finite field \mathbbF_q. In this article, we investigate the existence of m elements in arithmetic progression, where every element is primitive and at least one is normal with prescribed norms. Moreover, for n≥6,q=3^k,m=2 we establish that there are only 10 possible exceptions.

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