computational complexity

, Volume 6, Issue 1, pp 64–99 | Cite as

Counting curves and their projections

  • Joachim von zur Gathen
  • Marek Karpinski
  • Igor Shparlinski


Some deterministic and probabilistic methods are presented for counting and estimating the number of points on curves over finite fields, and on their projections. The classical question of estimating the size of the image of a univariate polynomial is a special case. For curves given by sparse polynomials, the counting problem is #P-complete via probabilistic parsimonious Turing reductions.


Computational Mathematic Problem Complexity Probabilistic Method Algorithm Analysis Finite Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Birkhäuser Verlag 1997

Authors and Affiliations

  • Joachim von zur Gathen
    • 1
  • Marek Karpinski
    • 3
  • Igor Shparlinski
    • 2
  1. 1.Department of Computer ScienceUniversity of TorontoTorontoCanada
  2. 2.School of MPCEMacquarie UniversitySydneyAustralia
  3. 3.Department of Computer ScienceUniversity of BonnBonnGermany

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