Geodesic
H.~Weyl asymptotics and Rankin convolutions
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 10, Tome 305 (2003), pp. 44-59

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Well-known H. Weyl asymptotics for eigenvalues is obtained by the arithmetic method. For congruence groups, the remainder in this asymptotics is a square root of the principal term. 
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     title = {H.~Weyl asymptotics and {Rankin} convolutions},
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A. I. Vinogradov. H.~Weyl asymptotics and Rankin convolutions. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 10, Tome 305 (2003), pp. 44-59. http://geodesic.mathdoc.fr/item/ZNSL_2003_305_a2/