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arXiv · 2306.10148

On real analogues of the Poincar\'e series

A. Campillo·F. Delgado·S. M. Gusein-Zade
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Abstract

There exist several equivalent equations for the Poincar\'e series of a collection of valuations on the ring of germs of functions on a complex analytic variety. We give definitions of the Poinca\'e series of a collection of valuations in the real setting (i.e., on the ring of germs of functions on a real analytic variety), compute them for the case of one curve valuation on the plane and discuss some of their properties.

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A. Campillo, F. Delgado, S. M. Gusein-Zade. 2023-06-16. On real analogues of the Poincar\'e series. https://arxiv.org/abs/2306.10148

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