Exact evaluation of second moments associated with some families of curves over a finite field

Ravi Donepudi, Junxian Li, Alexandru Zaharescu

Research output: Contribution to journalArticle

Abstract

Let Fq be the finite field with q elements. Given an N-tuple Q∈FqN, we associate with it an affine plane curve CQ over Fq. We consider the distribution of the quantity q−#Cq,Q where #Cq,Q denotes the number of Fq-points of the affine curve CQ, for families of curves parameterized by Q. Exact formulae for first and second moments are obtained in several cases when Q varies over a subset of FqN. Families of Fermat type curves, Hasse–Davenport curves and Artin–Schreier curves are also considered and results are obtained when Q varies along a straight line.

Original languageEnglish (US)
Pages (from-to)331-355
Number of pages25
JournalFinite Fields and their Applications
Volume48
DOIs
StatePublished - Nov 2017

Keywords

  • Curves over finite fields
  • Exact formulae
  • Exponential sums
  • Families of polynomials

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Algebra and Number Theory
  • Engineering(all)
  • Applied Mathematics

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