On small zeros of quadratic forms over finite fields
type: Item
instance of: scholarly article
title: On small zeros of quadratic forms over finite fields
zbMATH Open document ID: 0671.10014
DOI: 10.1016/0022-314X(89)90074-7
published in: Journal of Number Theory
publication date: 1989-01-01T00:00:00Z
review text: \textit{D. R. Heath-Brown} proved [Glasg. Math. J. 27, 87--93 (1985; Zbl 0581.10008)] that a quadratic form \(Q\) over \({\mathbb Z}/p{\mathbb Z}\) in \(m\geq 4\) variables has a nontrivial zero \(x=(x_ 1,\dots, x_ m)\) \((0\leq x_ i<p)\) with \(\max (x_ i)\leq c p^{1/2} \log p\) (\(c\) an absolute constant). A generalization to finite fields has been given by \textit{J. Sander} [Small solutions of quadratic equations over finite fields (German), Diss. Hannover (1987; Zbl 0628.10022)]. In the present paper, the author proves (apparently independently) the same result as Sander by similar methods.
Mathematics Subject Classification ID: 11E04
Mathematics Subject Classification ID: 11T06
Mathematics Subject Classification ID: 11T23
zbMATH DE Number: 4097471
zbMATH Keywords: quadratic forms
zbMATH Keywords: finite fields
zbMATH Keywords: small solutions
zbMATH Keywords: nontrivial zero
author: Yuan Wang
reviewed by: Rainer Schulze-Pillot
MaRDI profile type: Publication
cites work: Small solutions of quadratic congruences
cites work: Q5588717
cites work: Q5690468
cites work: Q5666618
cites work: Equations over finite fields. An elementary approach
description: scientific article; zbMATH DE number 4097471