Computing Zeta Functions of Artin–schreier Curves over Finite Fields

DOI10.1112/S1461157000000681zbMath1067.11078OpenAlexW2061425254MaRDI QIDQ4827595

Daqing Wan, Alan G. B. Lauder

Publication date: 18 November 2004

Published in: LMS Journal of Computation and Mathematics (Search for Journal in Brave)

Full work available at URL: http://www.lms.ac.uk/jcm/5/lms2001-022/

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Curves over finite and local fields (11G20) Exponential sums (11T23) Computational aspects of algebraic curves (14Q05)

Related Items

Counting irreducible polynomials with prescribed coefficients over a finite field, A quasi quadratic time algorithm for hyperelliptic curve point counting, Approximating Euler products and class number computation in algebraic function fields, On the enumeration of irreducible polynomials over \(\mathrm{GF}(q)\) with prescribed coefficients, Families of Artin-Schreier curves with Cartier-Manin matrix of constant rank, Resolution of nonsingularities for Mumford curves, Computing zeta functions of nondegenerate hypersurfaces with few monomials, A Point Counting Algorithm Using Cohomology with Compact Support, Computing zeta functions of Artin-Schreier curves over finite fields. II, Counting points on \(C_{ab}\) curves using Monsky-Washnitzer cohomology

Cites Work

• Unnamed Item
• Unnamed Item
• Exponential sums and Newton polyhedra: cohomology and estimates
• Completely continuous endomorphisms of \(p\)-adic Banach spaces
• Hyperelliptic cryptosystems
• On fast multiplication of polynomials over arbitrary algebras
• \(p\)-adic Banach spaces and families of modular forms
• Counting points on elliptic curves over finite fields
• On the p-adic Theory of Exponential Sums
• On the Rationality of the Zeta Function of an Algebraic Variety