The distribution of values of short hybrid exponential sums on curves over finite fields

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Abstract

Let p be a prime number, X be an absolutely irreducible affine plane curve over Fp, and g, f ε Fp(x, y). We study the distribution of the values of the hybrid exponential sums sn = σ PiεX, n<x(Pi)≤n+H y(Pi)ε J X(g(Pi)) ψ(f(Pi)) on n ε I for some short interval I. We show that under some natural conditions the limiting distribution of the projections of the sum Sn, n ε I on any straight line through the origin is Gaussian as p tends to infinity.

Original languageEnglish (US)
Pages (from-to)155-174
Number of pages20
JournalMathematical Research Letters
Volume18
Issue number1
DOIs
StatePublished - Jan 2011

Keywords

  • Exponential sums
  • Gaussian distribution

ASJC Scopus subject areas

  • Mathematics(all)

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