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The Zeta Function of a Pair of Quadratic Forms |
Canad. Math. Bull. 44(2001), 242-256
Published:2001-06-01
Printed: Jun 2001
Printed: Jun 2001
- Laura Mann Schueller
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] |