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arXiv · 2506.02693

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

Antonio Campillo·Felix Delgado·Sabir Gusein-Zade
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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 Poincar\'e series and the classical Poincar\'e series of a valuation.

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Antonio Campillo, Felix Delgado, Sabir Gusein-Zade. 2025-06-03. Poincar\'e series of valuations on functions over a field. https://arxiv.org/abs/2506.02693

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