Abstract.
We prove that the explicit formula in a symmetric case for a triple (Z, \(\tilde{Z}\), Φ) in Jorgenson-Lang’s fundamental class of functions holds for a larger class of (not necessarily differentiable or even continuous) test functions. As one of the most important applications, we show that the Selberg trace formula for a strictly hyperbolic cocompact Fuchsian group Γ is valid for a larger class of test functions. Further applications to growth estimates for the logarithmic derivative of the Selberg zeta function are considered.
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Avdispahić, M., Smajlović, L. An Explicit Formula and its Application to the Selberg Trace Formula. Mh Math 147, 183–198 (2006). https://doi.org/10.1007/s00605-005-0317-0
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DOI: https://doi.org/10.1007/s00605-005-0317-0