Geodesic
Expansion of automorphic functions
Zapiski Nauchnykh Seminarov POMI, Integral lattices and finite linear groups, Tome 116 (1982), pp. 119-141

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This paper proposes a method of expansion for automorphic functions on Lie groups, which generalizes the usual Fourier series expansion of automorphic functions on $SL_2(\mathbf R)/SO(2)$. Detailed consideration is given to the special case of the expansion of functions on $SL_3(\mathbf R)/SO(3)$, which are automorphic with respect to $SL_3(\mathbf Z)$. 
@article{ZNSL_1982_116_a12,
     author = {N. V. Proskurin},
     title = {Expansion of automorphic functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {119--141},
     publisher = {mathdoc},
     volume = {116},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1982_116_a12/}
}
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N. V. Proskurin. Expansion of automorphic functions. Zapiski Nauchnykh Seminarov POMI, Integral lattices and finite linear groups, Tome 116 (1982), pp. 119-141. http://geodesic.mathdoc.fr/item/ZNSL_1982_116_a12/