Igusa's local zeta functions of semiquasihomogeneous polynomials

DOI10.1090/S0002-9947-01-02323-6zbMath1007.11072arXivmath/9909184MaRDI QIDQ2716135

Wilson A. Zuniga-Galindo

Publication date: 6 June 2001

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9909184

zbMATH Keywords

local zeta functionssemiquasihomogeneous polynomials

Mathematics Subject Classification ID

Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Zeta functions and (L)-functions (11S40) Zeta and (L)-functions in characteristic (p) (11M38)

Related Items (17)

The motivic Igusa zeta series of some hypersurfaces non-degenerated with respect to their Newton polyhedron ⋮ Applications of an elementary resolution of singularities algorithm to exponential sums and congruences modulo \(p^n\) ⋮ A new generating function for calculating the Igusa local zeta function ⋮ Local zeta function for curves, non-degeneracy conditions and Newton polygons ⋮ Local zeta functions and Newton polyhedra ⋮ Monodromy conjecture for semi‐quasihomogeneous hypersurfaces ⋮ Poles of the Igusa local zeta function of some hybrid polynomials ⋮ Riesz kernels and pseudodifferential operators attached to quadratic forms over \(p\)-adic fields ⋮ Corrigendum to ``Decay of solutions of wave-type pseudo-differential equations over \(p\)-adic fields ⋮ Local zeta functions, pseudodifferential operators and Sobolev-type spaces over non-Archimedean local fields ⋮ Multiparametric exponential sums associated with quasi-homogeneous polynomial mappings ⋮ Decay of solutions of wave-type pseudo-differential equations over \(p\)-adic fields ⋮ Parabolic equations and Markov processes over \(p\)-adic fields ⋮ Regularization of \(p\)-adic string amplitudes, and multivariate local zeta functions ⋮ Local zeta functions and fundamental solutions for pseudo-differential operators over \(p\)-adic fields ⋮ Pseudo-differential equations connected with p-adic forms and local zeta functions ⋮ Exponential sums along \(p\)-adic curves.

Cites Work

• The rationality of the Poincaré series associated to the p-adic points on a variety
• Numbers of solutions of congruences: Poincaré series for algebraic curves
• Algorithme de calcul du polynome de Bernstein. Cas non dégéneré. (Algorithm of computation of Bernstein polynomials. The non-degenerate case)
• On the poles of a local zeta function for curves
• Fonctions d'Igusa p-adiques, polynômes de Bernstein, et polyèdres de Newton.
• On the Poincare Series for Diagonal Forms
• Complex powers and asymptotic expansions. II.
• Dedekind Sums for a Fuchsian Group, I
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