Taking advantage of methods originating with quantization theory, we try to get some better hold - if not an actual construction - of Maass (non-holomorphic) cusp-forms. We work backwards, from the rather simple results to the mostly devious road used to prove them.
@incollection{JEDP_1999____A15_0, author = {Andr\'e Unterberger}, title = {From pseudodifferential analysis to modular form theory}, booktitle = {}, series = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {15}, pages = {1--11}, publisher = {Universit\'e de Nantes}, year = {1999}, mrnumber = {1719006}, language = {en}, url = {https://proceedings.centre-mersenne.org/item/JEDP_1999____A15_0/} }
André Unterberger. From pseudodifferential analysis to modular form theory. Journées équations aux dérivées partielles (1999), article no. 15, 11 p. https://proceedings.centre-mersenne.org/item/JEDP_1999____A15_0/
[1] D. Bump, Automorphic Forms and Representations, Cambridge Series in Adv. Math. 55, Cambridge, 1996. | MR | Zbl
[2] H. Cohen, Sums involving the values at negative integers of L-functions of quadratic characters, Math. Ann. 217 (1975), 271-295. | MR | Zbl
[3] P.D. Lax, R.S. Phillips, Scattering Theory for Automorphic Functions, Ann. Math. Studies 87, Princeton Univ. Press, 1976. | MR | Zbl
[4] A. Terras, Harmonic analysis on symmetric spaces and applications 1, Springer-Verlag, New York-Berlin-Heidelberg-Tokyo, 1985. | MR | Zbl
[5] A. Unterberger, J. Unterberger, Algebras of Symbols and Modular Forms, J. d'Analyse Math. 68 (1996), 121-143. | MR | Zbl