JournalsjstVol. 6, No. 2pp. 267–329

Symmetry reduction of holomorphic iterated function schemes and factorization of Selberg zeta functions

  • David Borthwick

    Emory University, Atlanta, USA
  • Tobias Weich

    Universität Paderborn, Germany
Symmetry reduction of holomorphic iterated function schemes and factorization of Selberg zeta functions cover
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Abstract

Given a holomorphic iterated function scheme with a finite symmetry group GG, we show that the associated dynamical zeta function factorizes into symmetry-reduced analytic zeta functions that are parametrized by the unitary irreducible representations of GG. We show that this factorization implies a factorization of the Selberg zeta function on symmetric nn-funneled surfaces and that the symmetry factorization simplifies the numerical calculations of the resonances by several orders of magnitude. As an application this allows us to provide a detailed study of the spectral gap and we observe for the first time the existence of a macroscopic spectral gap on Schottky surfaces.

Cite this article

David Borthwick, Tobias Weich, Symmetry reduction of holomorphic iterated function schemes and factorization of Selberg zeta functions. J. Spectr. Theory 6 (2016), no. 2, pp. 267–329

DOI 10.4171/JST/125