Computing zeta functions of nondegenerate curves

DOI10.1155/IMRP/2006/72017zbMath1161.14302arXivmath/0607308MaRDI QIDQ3433122

Wouter Castryck, Jan Denef, Frederik Vercauteren

Publication date: 19 April 2007

Published in: International Mathematics Research Papers (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607308

zbMATH Keywords

computation of Hasse-Weil zeta-function

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Other Dirichlet series and zeta functions (11M41) Curves over finite and local fields (11G20) Finite ground fields in algebraic geometry (14G15) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10)

Related Items (24)

Models of curves over discrete valuation rings ⋮ Computing zeta functions of arithmetic schemes ⋮ Counting points on curves using a map to \(\mathbf P^1\). II. ⋮ Approximating Euler products and class number computation in algebraic function fields ⋮ Faster \(p\)-adic feasibility for certain multivariate sparse polynomials ⋮ Some variants of Macaulay's and Max Noether's theorems ⋮ Computing zeta functions of superelliptic curves in larger characteristic ⋮ Zeta-functions of curves of genus 3 over finite fields ⋮ Computing zeta functions of cyclic covers in large characteristic ⋮ Counting roots for polynomials modulo prime powers ⋮ Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in \(p\)-adic cohomology ⋮ Sparse effective membership problems via residue currents ⋮ An extension of Kedlaya's algorithm for hyperelliptic curves ⋮ Computing Zeta Functions in Families of C a,b Curves Using Deformation ⋮ On infiniteness of integral overconvergent de Rham-Witt cohomology modulo torsion ⋮ Algebraic independence in positive characteristic: A $p$-adic calculus ⋮ Toric forms of elliptic curves and their arithmetic ⋮ Fast arithmetic in unramified \(p\)-adic fields ⋮ Explicit Coleman Integration for Hyperelliptic Curves ⋮ Computing zeta functions of generic projective hypersurfaces in larger characteristic ⋮ Counting points on curves using a map to $\mathbf {P}^1$ ⋮ Curves in characteristic \(2\) with non-trivial \(2\)-torsion ⋮ Randomized polynomial-time root counting in prime power rings ⋮ Computing zeta functions of algebraic curves using Harvey's trace formula

This page was built for publication: Computing zeta functions of nondegenerate curves