Une estimation asymptotique du nombre de solutions approchées d'une équation p-adique. (Asymptotic estimation of the number of approximate solutions of a p-adic equation)

DOI10.1007/BF01388790zbMath0607.12008OpenAlexW2091619878MaRDI QIDQ1085208

François Loeser

Publication date: 1986

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143357

zbMATH Keywords

asymptotic expansionspolar invariantsHodge theoryNewton polyhedranumber of roots of p-adic equation

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Equations in general fields (12E12) Local ground fields in algebraic geometry (14G20) Zeta functions and (L)-functions (11S40) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30)

Related Items (2)

Mixed Łojasiewicz exponents and \(\log\) canonical thresholds of ideals ⋮ Zeta functions for analytic mappings, log-principalization of ideals, and Newton polyhedra

Cites Work

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• Some local consequences of Hodge theory
• Lectures on forms of higher degree. Notes by S. Raghavan
• Semicontinuity of the singularity spectrum
• Variétés polaires. I: Invariants polaires des singularites d'hypersurfaces
• The complex exponent of a singularity does not change along strata mu=const
• Newton polyhedra and estimation of oscillating integrals
• Stable structures on manifolds. I: Homeomorphismus of \(S^ n\). II: Stable manifolds. III: Applications
• Some Observations on Higher Degree Characters
• Complex powers and asymptotic expansions. I. Functions of certain types.

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