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Hierarchy of the Selberg Zeta Functions

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Abstract

We introduce a Selberg type zeta function of two variables which interpolates several higher Selberg zeta functions. The analytic continuation, the functional equation and the determinant expression of this function via the Laplacian on a Riemann surface are obtained.

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Authors and Affiliations

  1. Graduate School of Mathematics, Kyushu University, 6-10-1, Hakozaki, Fukuoka, 812-8581, Japan

    Yasufumi Hashimoto

  2. Faculty of Mathematics, Kyushu University, 6-10-1, Hakozaki, Fukuoka, 812-8581, Japan

    Masato Wakayama

Authors
  1. Yasufumi Hashimoto
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  2. Masato Wakayama
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Correspondence to Yasufumi Hashimoto.

Additional information

Mathematics Subject Classifications (2000). Primary 11M36, Secondary 33B15

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Hashimoto, Y., Wakayama, M. Hierarchy of the Selberg Zeta Functions. Lett Math Phys 73, 59–70 (2005). https://doi.org/10.1007/s11005-005-6784-3

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  • DOI: https://doi.org/10.1007/s11005-005-6784-3

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