TY - JOUR
T1 - Poisson type phenomena for points on hyperelliptic curves modulo p
AU - Mak, Kit Ho
AU - Zaharescu, Alexandru
N1 - Funding Information:
The second author is supported by NSF grant number DMS - 0901621.
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
KW - Hyperelliptic curves
KW - Poisson distribution
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U2 - 10.7169/facm/2012.47.1.5
DO - 10.7169/facm/2012.47.1.5
M3 - Article
AN - SCOPUS:84983457489
VL - 47
SP - 65
EP - 78
JO - Functiones et Approximatio, Commentarii Mathematici
JF - Functiones et Approximatio, Commentarii Mathematici
SN - 0208-6573
IS - 1
ER -