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arxiv: 2506.02693 · v2 · submitted 2025-06-03 · 🧮 math.AG

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Poincar\'e series of valuations on functions over a field

Antonio Campillo , Felix Delgado , Sabir Gusein-Zade
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classification 🧮 math.AG
keywords seriespoincarfieldvaluationsalgebraclassicalcoeficientscomplex
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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 Poincar\'e series and the classical Poincar\'e series of a valuation.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. On a generalized Poincar\'e series of plane valuations

    math.AG 2026-05 unverdicted novelty 5.0

    Equations are given for the generalized Poincaré series of plane valuations on E_{K^2,0} using the generalized Euler characteristic integral over the projectivized extended semigroup.