On the set of critical exponents of discrete groups acting on regular trees
J. Korean Math. Soc. 2019 Vol. 56, No. 2, 475-484
Published online 2019 Mar 01
Sanghoon Kwon
Catholic Kwandong University
Abstract : We study the set of critical exponents of discrete groups acting on regular trees. We prove that for every real number $\delta$ between $0$ and $\frac{1}{2}\log q$, there is a discrete subgroup $\Gamma$ acting without inversion on a $(q+1)$-regular tree whose critical exponent is equal to $\delta$. Explicit construction of edge-indexed graphs corresponding to a quotient graph of groups are given.
Keywords : groups acting on trees, critical exponents, Ihara zeta function
MSC numbers : Primary 20E08; Secondary 05E18, 57M60
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