We develop efficient methods for deterministic computations with semi-algebraic sets and apply them to the problem of counting points on curves and Abelian varieties over finite fields. For Abelian varieties of dimension g in projective N space over Fq, we improve Pila's result and show that the pro
โฆ LIBER โฆ
Explicit bounds of polynomial coefficients and counting points on Picard curves over finite fields
โ Scribed by Gyoyong Sohn; Hoil Kim
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 517 KB
- Volume
- 49
- Category
- Article
- ISSN
- 0895-7177
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The number of points on the curve aY e =bX e +c (abc{0) defined over a finite field F q , q#1 (mod e), is known to be obtainable in terms of Jacobi sums and cyclotomic numbers of order e with respect to this field. In this paper, we obtain explicitly the Jacobi sums and cyclotomic numbers of order e