[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j180226

ON THE SET OF CRITICAL EXPONENTS OF DISCRETE GROUPS ACTING ON REGULAR TREES

Kwon, Sanghoon (Department of Mathematical Education Catholic Kwandong University)

Publication Information

Journal of the Korean Mathematical Society / v.56, no.2, 2019 , pp. 475-484 More about this Journal

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;

Citations & Related Records

Reference

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