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

✍ Scribed by David B. Leep; Laura Mann Schueller

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 155 KB
Volume: 5
Category: Article
ISSN: 1071-5797
DOI: 10.1006/ffta.1998.0232

No coin nor oath required. For personal study only.

✦ Synopsis

Let N be the number of affine zeros of a pair of quadratic forms in n#1 variables defined over a finite field F O . We give upper and lower bounds for N and show that these bounds are optimal. One result states that if n#1510 and every quadratic form in the pencil has order at least three, then "N!qL"(qL.

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