Geodesic
Asymptotic behaviour of the~spectral function of the~Laplace--Beltrami operator for cocompact discrete subgroups of $\operatorname {SL}_2(\mathbb R)$
Sbornik. Mathematics, Tome 189 (1998) no. 7, pp. 977-990

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An asymptotic formula, uniform in $z$ and $z'$, is obtained for the spectral function $\theta (z,z',\lambda )$ of the Laplace–Beltrami operator for cocompact discrete subgroups of $\operatorname {SL}_2(\mathbb R)$ with power-law lowering of the order of the remainder. 
@article{SM_1998_189_7_a1,
     author = {V. V. Golovchanskii},
     title = {Asymptotic behaviour of the~spectral function of {the~Laplace--Beltrami} operator for cocompact discrete subgroups of $\operatorname {SL}_2(\mathbb R)$},
     journal = {Sbornik. Mathematics},
     pages = {977--990},
     publisher = {mathdoc},
     volume = {189},
     number = {7},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1998_189_7_a1/}
}
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V. V. Golovchanskii. Asymptotic behaviour of the~spectral function of the~Laplace--Beltrami operator for cocompact discrete subgroups of $\operatorname {SL}_2(\mathbb R)$. Sbornik. Mathematics, Tome 189 (1998) no. 7, pp. 977-990. http://geodesic.mathdoc.fr/item/SM_1998_189_7_a1/