Let E be an elliptic curve defined over Q and without complex multiplication. For a prime p of good reduction, let % E E be the reduction of E modulo p: Assuming that certain Dedekind zeta functions have no zeros in ReðsÞ > 3=4; we determine how often % E EðF p Þ is a cyclic group. This result was p
The Number of Rational Points of a Class of Artin–Schreier Curves
✍ Scribed by Robert S Coulter
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 172 KB
- Volume
- 8
- Category
- Article
- ISSN
- 1071-5797
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✦ Synopsis
We determine the number of F q -rational points of a class of Artin-Schreier curves by using recent results concerning evaluations of some exponential sums. In particular, we determine infinitely many new examples of maximal and minimal plane curves in the context of the Hasse-Weil bound. # 2002 Elsevier Science (USA)
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