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More Points Than Expected on Curves over Finite Field Extensions

✍ Scribed by Bradley W. Brock; Andrew Granville

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 196 KB
Volume: 7
Category: Article
ISSN: 1071-5797
DOI: 10.1006/ffta.2000.0308

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✦ Synopsis

On average, there are qP#o (qP) F qP -rational points on curves of genus g de"ned over F O P . This is also true if we restrict our average to genus g curves de"ned over F O , provided r is odd or r'2g. However, if r"2, 4, 6, 2 or 2g then the average is qP#qP#o(qP). We give a number of proofs of the existence of these qP extra points, and in some cases give a precise formula, but we are unable to provide a satisfactory explanation for this phenomenon.

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