Geodesic
The Zeta Function of a Pair of Quadratic Forms
Canadian mathematical bulletin, Tome 44 (2001) no. 2, pp. 242-256

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DOI

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 char $k\,\ne \,2$ . 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 established.
DOI : 10.4153/CMB-2001-024-7
Mots-clés : 11G25 
Schueller, Laura Mann. The Zeta Function of a Pair of Quadratic Forms. Canadian mathematical bulletin, Tome 44 (2001) no. 2, pp. 242-256. doi: 10.4153/CMB-2001-024-7
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     title = {The {Zeta} {Function} of a {Pair} of {Quadratic} {Forms}},
     journal = {Canadian mathematical bulletin},
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     year = {2001},
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     number = {2},
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2001-024-7/}
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