Poisson type phenomena for points on hyperelliptic curves modulo p

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Abstract

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 languageEnglish (US)
Pages (from-to)65-78
Number of pages14
JournalFunctiones et Approximatio, Commentarii Mathematici
Volume47
Issue number1
DOIs
StatePublished - 2012

Keywords

  • Hyperelliptic curves
  • Poisson distribution

ASJC Scopus subject areas

  • Mathematics(all)

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