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# The Zeta Function of a Pair of Quadratic Forms

Published:2001-06-01
Printed: Jun 2001
• Laura Mann Schueller
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## Abstract

The zeta function of a nonsingular pair of quadratic forms defined over a finite field, $k$, of arbitrary characteristic is calculated. A.~Weil made this computation when $\rmchar k \neq 2$. When the pair has even order, a relationship between the number of zeros of the pair and the number of places of degree one in an appropriate hyperelliptic function field is
 MSC Classifications: 11G25 - Varieties over finite and local fields [See also 14G15, 14G20]