Zeros of a Pair of Quadratic Forms Defined over a Finite Field

David B. Leep; Laura Mann Schueller

doi:10.1006/ffta.1998.0232

Zeros of a Pair of Quadratic Forms Defined over a Finite Field

David B. Leep, Laura Mann Schueller

Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

LetNbe the number of affine zeros of a pair of quadratic forms inn+1 variables defined over a finite fieldF_q. We give upper and lower bounds forNand show that these bounds are optimal. One result states that ifn+1≥10 and every quadratic form in the pencil has order at least three, then N-q^n-1<q^n-2.

Original language	English
Pages (from-to)	157-176
Number of pages	20
Journal	Finite Fields and Their Applications
Volume	5
Issue number	2
DOIs	https://doi.org/10.1006/ffta.1998.0232
State	Published - Apr 1999

ASJC Scopus subject areas

Theoretical Computer Science
Algebra and Number Theory
General Engineering
Applied Mathematics

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10.1006/ffta.1998.0232

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title = "Zeros of a Pair of Quadratic Forms Defined over a Finite Field",

abstract = "LetNbe the number of affine zeros of a pair of quadratic forms inn+1 variables defined over a finite fieldFq. We give upper and lower bounds forNand show that these bounds are optimal. One result states that ifn+1≥10 and every quadratic form in the pencil has order at least three, then N-qn-1n-2.",

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AU - Schueller, Laura Mann

PY - 1999/4

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N2 - LetNbe the number of affine zeros of a pair of quadratic forms inn+1 variables defined over a finite fieldFq. We give upper and lower bounds forNand show that these bounds are optimal. One result states that ifn+1≥10 and every quadratic form in the pencil has order at least three, then N-qn-1n-2.

AB - LetNbe the number of affine zeros of a pair of quadratic forms inn+1 variables defined over a finite fieldFq. We give upper and lower bounds forNand show that these bounds are optimal. One result states that ifn+1≥10 and every quadratic form in the pencil has order at least three, then N-qn-1n-2.

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JO - Finite Fields and Their Applications

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Zeros of a Pair of Quadratic Forms Defined over a Finite Field

Abstract

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