Let p be a large prime, and let C be a hyperelliptic curve over Fp. We study the distribution of the x-coordinates in short intervals when the y-coordinates lie in a prescribed interval, and the distribution of the distance between consecutive x-coordinates with the same property. Next, let g(P, P0) be a rational function of two points on C. We study the distribution of the above distances with an extra condition that g(Pi, Pi+1) lies in a prescribed interval, for any consecutive points Pi, Pi+1.
|Original language||English (US)|
|Number of pages||14|
|Journal||Functiones et Approximatio, Commentarii Mathematici|
|State||Published - 2012|
- Hyperelliptic curves
- Poisson distribution
ASJC Scopus subject areas