Exotic approximate identities and Maass forms
Volume 159 / 2013
Acta Arithmetica 159 (2013), 27-46
MSC: Primary 11F72; Secondary 11N75, 33F05, 41A80.
DOI: 10.4064/aa159-1-2
Abstract
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.
