Local zeta functions and Newton polyhedra

DOI10.1017/S0027763000008631zbMath1063.11048arXivmath/0204241MaRDI QIDQ4822299

Wilson A. Zuniga-Galindo

Publication date: 25 October 2004

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0204241

zbMATH Keywords

Igusa's local zeta function

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 (13)

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 ⋮ Poles of the Igusa local zeta function of some hybrid polynomials ⋮ Igusa’s Local Zeta Functions and Exponential Sums for Arithmetically Non Degenerate Polynomials ⋮ 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 ⋮ Pseudo-differential equations connected with p-adic forms and local zeta functions ⋮ Zeta functions for analytic mappings, log-principalization of ideals, and Newton polyhedra ⋮ An explicit formula for the local zeta function of a Laurent polynomial ⋮ Exponential sums along \(p\)-adic curves.

Cites Work

• Polyèdre de Newton et distribution \(f^ s_+\). I. (Newton polyhedra and distributions \(f^ s_+\). I.)
• The rationality of the Poincaré series associated to the p-adic points on a variety
• On the poles of a local zeta function for curves
• Newton polyhedron and \(f^ s_ +\) distribution. II
• Newton polyhedra and estimation of oscillating integrals
• Newton polyhedra and Igusa's local zeta function
• Igusa's local zeta functions of semiquasihomogeneous polynomials

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