Deformation theory and the computation of zeta functions

DOI10.1112/S0024611503014461zbMath1119.11053OpenAlexW2063328473MaRDI QIDQ4812523

Alan G. B. Lauder

Publication date: 23 August 2004

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/s0024611503014461

Mathematics Subject Classification ID

Exponential sums (11T23) Zeta and (L)-functions in characteristic (p) (11M38)

Related Items (21)

Frobenius structures on hypergeometric equations ⋮ Rigid cohomology and \(p\)-adic point counting ⋮ A one parameter family of Calabi-Yau manifolds with attractor points of rank two ⋮ Zeta functions of monomial deformations of Delsarte hypersurfaces ⋮ Improved complexity bounds for counting points on hyperelliptic curves ⋮ Improvements to the deformation method for counting points on smooth projective hypersurfaces ⋮ Genus 2 point counting over prime fields ⋮ Computing zeta functions of superelliptic curves in larger characteristic ⋮ Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in \(p\)-adic cohomology ⋮ Computing Zeta Functions in Families of C a,b Curves Using Deformation ⋮ Point counting in families of hyperelliptic curves ⋮ Fast arithmetic in unramified \(p\)-adic fields ⋮ Explicit Coleman Integration for Hyperelliptic Curves ⋮ Computing zeta functions of generic projective hypersurfaces in larger characteristic ⋮ MEMORY EFFICIENT HYPERELLIPTIC CURVE POINT COUNTING ⋮ Counting points on hyperelliptic curves with explicit real multiplication in arbitrary genus ⋮ Point Counting in Families of Hyperelliptic Curves in Characteristic 2 ⋮ A Point Counting Algorithm Using Cohomology with Compact Support ⋮ Quasi-quadratic elliptic curve point counting using rigid cohomology ⋮ Two Recent p-adic Approaches Towards the (Effective) Mordell Conjecture ⋮ Tracking -adic precision

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