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 -