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Selberg Zeta Function

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Spectral Theory of Infinite-Area Hyperbolic Surfaces

Part of the book series: Progress in Mathematics ((PM,volume 318))

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Abstract

For a geometrically finite hyperbolic surface X the Selberg zeta function Z X (s) was introduced in §2.5. The zeta function is associated with the length spectrum of X (or, equivalently, to traces of conjugacy classes of Γ). We will see in this chapter that it deserves to be thought of as a spectral invariant as well, by virtue of a beautiful correspondence between resonances of X and the zeros of Z X (s).

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Emory University, Atlanta, GA, USA

    David Borthwick

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  1. David Borthwick
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Borthwick, D. (2016). Selberg Zeta Function. In: Spectral Theory of Infinite-Area Hyperbolic Surfaces. Progress in Mathematics, vol 318. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-33877-4_10

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