Poincaré series of valuations on functions over a field

2025/06/03 by Antonio Campillo, Campillo, Antonio, F. Delgado +3
Mathematics · #14B05 #14G27 #16W60 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2506.02693

openalex publication_date 2025/06/03 · openalex created_date 2025/10/14 · openalex updated_date 2026/08/01

Abstract

For a subfield \K of the field \C of complex numbers, we consider curve and divisorial valuations on the algebra \K[[x,y]] of formal power series in two variables with the coeficients in \K. We compute the semigroup Poincaré series and the classical Poincaré series of a valuation.

Citations

• Real Poincaré series of a plane divisorial valuation
• On the topological type of a set of plane valuations with symmetries
• Generating sequences and Poincaré series for a finite set of plane divisorial valuations

Related

• Real Poincaré series of a plane divisorial valuation
• Poincare Series of Non-divisorial Valuations on Two-dimensional Function Fields
• On real analogues of the Poincaré series
• Generating sequences and Poincaré series for a finite set of plane divisorial valuations
• The Poincare series of divisorial valuations in the plane defines the topology of the set of divisors