Local and global zeta-functions of singular algebraic curves

DOI10.1006/jnth.1998.2240zbMath0940.14016OpenAlexW2061286140MaRDI QIDQ1273704

Karl-Otto Stöhr

Publication date: 11 July 2000

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.1998.2240

zbMATH Keywords

functional equationRiemann hypothesessingular curveGorenstein curvenumber of rational points on the compactified Jacobianzeta function of Gorenstein ring

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10)

Related Items (10)

On trigonal non-Gorenstein curves with zero Maroni invariant ⋮ Multi-variable Poincaré series of algebraic curve singularities over finite fields ⋮ On Weierstrass semigroups at one and two points and their corresponding Poincaré series ⋮ The analytic class number formula for 1‐dimensional affine schemes ⋮ Motivic zeta functions for curve singularities ⋮ Fractional ideals and integration with respect to the generalised Euler characteristic ⋮ On the relation between the generalized Poincaré series and the Stöhr zeta function ⋮ Gröbner cells of punctual Hilbert schemes in dimension two ⋮ The local and global zeta functions of Gauss's curve ⋮ On Poincaré series of singularities of algebraic curves over finite fields

Cites Work

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• Gorenstein curves and symmetry of the semigroup of values
• Functional equations for zeta functions of non-Gorenstein orders in global fields
• On the singularity degree of subrings in function fields
• Semigroup of two irreducible algebroid plane curves
• Very ampleness for Theta on the compactified Jacobian
• Zeta functions and Cartier divisors on singular curves over finite fields
• Analytische Zahlentheorie in Körpern der Charakteristik \(p\)
• Der kanonische Modul eines Cohen-Macaulay-Rings. (The canonical moduls of a Cohen-Macaulay-ring)
• On the arithmetic genera and the effective genera of algebraic curves
• Semigroups associated to singular points of plane curves.
• On the poles of regular differentials of singular curves
• The Value-Semigroup of a One-Dimensional Gorenstein Ring

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