Geodesic
One a type of automorphic forms
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 20, Tome 201 (1992), pp. 177-189 
N. A. Shirokov. One a type of automorphic forms. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 20, Tome 201 (1992), pp. 177-189. http://geodesic.mathdoc.fr/item/ZNSL_1992_201_a7/
@article{ZNSL_1992_201_a7,
     author = {N. A. Shirokov},
     title = {One a type of automorphic forms},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {177--189},
     year = {1992},
     volume = {201},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1992_201_a7/}
}
TY  - JOUR
AU  - N. A. Shirokov
TI  - One a type of automorphic forms
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1992
SP  - 177
EP  - 189
VL  - 201
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1992_201_a7/
LA  - ru
ID  - ZNSL_1992_201_a7
ER  - 
%0 Journal Article
%A N. A. Shirokov
%T One a type of automorphic forms
%J Zapiski Nauchnykh Seminarov POMI
%D 1992
%P 177-189
%V 201
%U http://geodesic.mathdoc.fr/item/ZNSL_1992_201_a7/
%G ru
%F ZNSL_1992_201_a7

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The aim of the paper is to construct а $\Gamma$-automorphic form of weight $-2k$ for a given finitely generated Fuchsian group $\Gamma$ of the second kind. The construction heavily relies on important properties of the outer function introduced by Widom that have been established by the author. The $\Gamma$-automorphic form construced possesses the highest possible smoothness for the weight $-2k$.