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arXiv · 2507.15394

Tauberian Theorem: Square-root singularity and Ramified covering of degree two

Guillaume Chevalier
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Abstract

We prove a Tauberian theorem concerning power series admitting square root singularities. More precisely we give an asymptotic expansion to any order of the coefficients of a power series admitting square-root type singularities. This article is one of a triptych with [Che25b] and [Che25c] that aims at proving an asympototic expansion to any order of the passage probability of an irreducible finite range random walk on free groups.

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Guillaume Chevalier. 2025-07-21. Tauberian Theorem: Square-root singularity and Ramified covering of degree two. https://arxiv.org/abs/2507.15394

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