期刊
FINITE FIELDS AND THEIR APPLICATIONS
卷 7, 期 1, 页码 70-91出版社
ACADEMIC PRESS INC
DOI: 10.1006/ffta.2000.0308
关键词
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On average, there are q(r) + o(q(r/2)) F-q-rational points on curves of genus g defined over F-qr. This is also true if we restrict our average to genus g curves defined over F-q, provided r is odd or r > 2g. However, if r = 2,4,6,... or 2g then the average is q(r) + q(r/2) + o(q(r/2)). We give a number of proofs of the existence of these q(r/2) extra points, and in some cases give a precise formula, but we are unable to provide a satisfactory explanation for this phenomenon. (C) 2000 Academic Press.
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