Jacobsthal sums of prime order
type: Item
instance of: scholarly article
title: Jacobsthal sums of prime order
zbMATH Open document ID: 0605.10020
author: S. A. Katre
author: A. R. Rajwade
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Let \(p\) be an odd prime and let \(q=p^{\alpha}\), where \(\alpha\geq 1\). For \(a\in \mathrm{GF}(q)\) and \(e\geq 1\) the Jacobsthal sum \(\Phi_e(a)\) of order \(e\) is defined by \[ \Phi_e(a)=\sum_{x\in \mathrm{GF}(q)}\left(\frac{x}{q}\right)\left(\frac{x^e+a}{q}\right), \] where \((\frac{.}{q})\) is the Legendre symbol for \(\mathrm{GF}(q)\). The authors evaluate \(\Phi_e(a)\), for any odd prime \(e\), in terms of the solutions of an appropriate quadratic partition of \(q\).
Mathematics Subject Classification ID: 11L10
zbMATH DE Number: 3977093
zbMATH Keywords: evaluation
zbMATH Keywords: quadratic partition of primes
zbMATH Keywords: Jacobsthal sum
zbMATH Keywords: Legendre symbol
reviewed by: Kenneth S. Williams
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3977093