Abstract
In this chapter we derive the Selberg trace formula. We begin by describing it in a general framework which renders transparent the analogy with the Poisson summation formula recalled in the introduction. Having done so, the remaining work consists in explicating the general formula in the case of compact hyperbolic surfaces and then for the modular surface.
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Notes
- 1.
Why one uses this terminology will become clear in the next section.
- 2.
The function \(\varphi\) is then replaced by a matrix-valued function called the scattering matrix.
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Bergeron, N. (2016). The Trace Formula. In: The Spectrum of Hyperbolic Surfaces. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-27666-3_5
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