We obtain some approximate identities whose accuracy depends on the bottom of the discrete spectrum of the Laplace-Beltrami operator in the automorphic setting and on the symmetries of the corresponding Maass wave forms. From the geometric point of view, the underlying Riemann surfaces are classical modular curves and Shimura curves.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa159-1-2, author = {Fernando Chamizo and Dulcinea Raboso and Seraf\'\i n Ruiz-Cabello}, title = {Exotic approximate identities and Maass forms}, journal = {Acta Arithmetica}, volume = {161}, year = {2013}, pages = {27-46}, zbl = {1327.11036}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa159-1-2} }
Fernando Chamizo; Dulcinea Raboso; Serafín Ruiz-Cabello. Exotic approximate identities and Maass forms. Acta Arithmetica, Tome 161 (2013) pp. 27-46. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa159-1-2/