Computing zeta functions of generic projective hypersurfaces in larger characteristic

Jan Tuitman

Computing zeta functions of generic projective hypersurfaces in larger characteristic

Number Theory 2017-09-14 v3 Algebraic Geometry

Authors: Jan Tuitman

Abstract

We give improvements of the deformation method for computing the zeta function of a generic projective hypersurface in characteristic~ $p$ that either reduce the dependence on~ $p$ of the time complexity to $\tilde{O}(p^{1/2})$ or that of the space complexity to $\tilde{O}(\log(p))$ while remaining polynomial in the other input parameters.

Keywords

zeta functions projective hypersurfaces deformation method characteristic p time complexity space complexity algorithm improvement

Cite

@article{arxiv.1704.02306,
  title  = {Computing zeta functions of generic projective hypersurfaces in larger characteristic},
  author = {Jan Tuitman},
  journal= {arXiv preprint arXiv:1704.02306},
  year   = {2017}
}

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