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Zero is a resonance of every Schottky surface

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arxiv 1808.09239 v1 pith:LFQ4CW3R submitted 2018-08-28 math.SP

Alexander Adam , Anke Pohl , Alexander Wei{ss}e This is my paper · ORCID
classification math.SP
keywords schottkyzeroeveryresonancespectralsurfacecertaincomparing
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For certain spectral parameters we find explicit eigenfunctions of transfer operators for Schottky surfaces. Comparing the dimension of the eigenspace for the spectral parameter zero with the multiplicity of topological zeros of the Selberg zeta function, we deduce that zero is a resonance of every Schottky surface.

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  1. The divisor of the twisted Selberg zeta function

    math.SP 2026-07 accept novelty 7.0 of 10

    The divisor of the twisted Selberg zeta function of any geometrically finite infinite-area hyperbolic orbisurface decomposes explicitly into Laplace resonances, orbifold-point factors, Barnes G/gamma factors, and cusp...

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