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Computing Zeta Functions of Nondegenerate Curves
- Source :
- ResearcherID
- Publication Year :
- 2006
-
Abstract
- In this paper we present a p-adic algorithm to compute the zeta function of a nondegenerate curve over a finite field using Monsky-Washnitzer cohomology. The paper vastly generalizes previous work since all known cases, e.g. hyperelliptic, superelliptic and C_{ab} curves, can be transformed to fit the nondegenerate case. For curves with a fixed Newton polytope, the property of being nondegenerate is generic, so that the algorithm works for almost all curves with given Newton polytope. For a genus g curve over F_{p^n}, the expected running time is O(n^3g^6 + n^2g^{6.5}), whereas the space complexity amounts to O(n^3g^4), assuming p is fixed.<br />41 pages
- Subjects :
- Discrete mathematics
Pure mathematics
Work (thermodynamics)
Mathematics - Number Theory
General Mathematics
Polytope
Space (mathematics)
Cohomology
Running time
Riemann zeta function
symbols.namesake
Mathematics - Algebraic Geometry
Finite field
Genus (mathematics)
FOS: Mathematics
symbols
Number Theory (math.NT)
Algebraic Geometry (math.AG)
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- ResearcherID
- Accession number :
- edsair.doi.dedup.....1ddc9e9aa3f3a748edddeefcaf10c76b