Numbers of solutions of congruences: Poincaré series for algebraic curves

DOI10.1016/0001-8708(86)90088-5zbMath0606.12012OpenAlexW2022859156MaRDI QIDQ1084452

Jay R. Goldman

Publication date: 1986

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(86)90088-5

zbMATH Keywords

singularitiesPoincaré seriespolessystem of congruencesp-adic units

Mathematics Subject Classification ID

Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Singularities of curves, local rings (14H20) Zeta functions and (L)-functions (11S40)

Related Items (5)

Igusa's local zeta functions of semiquasihomogeneous polynomials ⋮ Série de Poincaré pour certaines courbes. (Poincaré series for certain curves) ⋮ ON MARKOFF–HURWITZ EQUATIONS OVER RESIDUE CLASS RINGS ⋮ Generalizations of the Markoff–Hurwitz equations over residue class rings ⋮ Newton polyhedra and Igusa's local zeta function

Cites Work

• Unnamed Item
• The rationality of the Poincaré series associated to the p-adic points on a variety
• Rationality criteria and application to the generating series of a system of equations with coefficients in a local field
• Reduction modulo \(p^ n\) des sous-ensembles analytiques fermés de \(\mathbb Z_p^N\).
• On the poles of a local zeta function for curves
• Numbers of Solutions of Congruences: Poincare Series for Strongly Nondegenerate Forms

This page was built for publication: Numbers of solutions of congruences: Poincaré series for algebraic curves