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Counting curves and their projections

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Abstract

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.

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Author notes

  1. Joachim von zur Gathen

    Present address: Fachbereich Mathematik-Informatik, Universität-GH Paderborn, D-33095, Paderborn, Germany

Authors and Affiliations

  1. Department of Computer Science, University of Toronto, M5S 1A4, Toronto, Ontario, Canada

    Joachim von zur Gathen

  2. School of MPCE, Macquarie University, NSW 2109, Sydney, Australia

    Igor Shparlinski

  3. Department of Computer Science, University of Bonn, 53117, Bonn, Germany

    Marek Karpinski

Authors
  1. Joachim von zur Gathen
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  2. Marek Karpinski
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  3. Igor Shparlinski
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von zur Gathen, J., Karpinski, M. & Shparlinski, I. Counting curves and their projections. Comput Complexity 6, 64–99 (1996). https://doi.org/10.1007/BF01202042

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  • DOI: https://doi.org/10.1007/BF01202042

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