Geodesic
The discrete spectrum of the Laplace operator on the fundamental domain of the modular group and the Chebyshev psi-function
Izvestiya. Mathematics , Tome 83 (2019) no. 5, pp. 1066-1079

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An explicit formula is obtained expressing the Chebyshev psi-function in terms of the discrete spectrum of the Laplace operator on the fundamental domain of the modular group.
Keywords: Selberg formula, spectrum of the Laplace operator, Chebyshev psi-function, modular group. 
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     author = {D. A. Popov},
     title = {The discrete spectrum of the {Laplace} operator on the fundamental domain of the modular group and the {Chebyshev} psi-function},
     journal = {Izvestiya. Mathematics },
     pages = {1066--1079},
     publisher = {mathdoc},
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     number = {5},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2019_83_5_a6/}
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D. A. Popov. The discrete spectrum of the Laplace operator on the fundamental domain of the modular group and the Chebyshev psi-function. Izvestiya. Mathematics , Tome 83 (2019) no. 5, pp. 1066-1079. http://geodesic.mathdoc.fr/item/IM2_2019_83_5_a6/