Heilbronn's conjecture on Waring's number (mod \(p\))
type: Item
instance of: scholarly article
title: Heilbronn's conjecture on Waring's number (mod \(p\))
zbMATH Open document ID: 1185.11025
author: James Cipra
author: Todd Cochrane
author: Chris Pinner
published in: Journal of Number Theory
publication date: 2007-09-13T00:00:00Z
review text: Let \(p\) be an odd prime number and \(H\) a subgroup of index \(d\) of \(\mathbb{Z}/p\mathbb{Z}\). The authors compute the ``\(g\)'' of the Waring's problem for the \(k =(p-1)/d\)-th powers when \(\Phi(d)=2\) and bound above \(g^q/k\), where \(q\) does not exceed \(\Phi(d),\) by a constant depending only on \(q\). For example it is proved that \(g(k,p)=a-1\) when \(d=4\) and the prime \(p\) is decomposed as \(p=(a+bi)(a-bi).\)
reviewed by: Luis Gallardo
Mathematics Subject Classification ID: 11D85
Mathematics Subject Classification ID: 11P05
zbMATH DE Number: 5190744
zbMATH Keywords: Warings's problem
zbMATH Keywords: prime field
MaRDI profile type: Publication
full work available at URL: j.jnt.2006.12.001
OpenAlex ID: W1972484768
Wikidata QID: Q122927566
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DOI: 10.1016/J.JNT.2006.12.001
description: scientific article; zbMATH DE number 5190744