Extended automorphic forms on the upper half plane
A variant of Hadamard's notion of partie finie is applied to the theory of automorphic functions on arithmetic quotients of the upper half-plane. As a consequence, conceptually simple proofs of the volume formula and the Maass-Selberg relations are given. This technique interprets \textit{D. Zagier's} idea of renormalization [J. Fac. Sci. Univ. Tokyo, Ser. I A 28, 415-437 (1982; Zbl 0505.10011)] so that it can be generalized easily to higher rank quotients (which is not done in this paper, however).
arithmetic quotients of the upper half-plane
scientific article; zbMATH DE number 537283
scientific article