Tauberian Theorem: Square-root singularity and Ramified covering of degree two
Complex Variables
2025-07-22 v1
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.
Cite
@article{arxiv.2507.15394,
title = {Tauberian Theorem: Square-root singularity and Ramified covering of degree two},
author = {Guillaume Chevalier},
journal= {arXiv preprint arXiv:2507.15394},
year = {2025}
}