modular forms, a Maass–Shimura operator is an operator which maps modular forms to almost holomorphic modular forms. The Maass–Shimura operator on (almost holomorphic)...

orthogonal Shimura varieties. A complex-valued smooth function f {\displaystyle f} on the upper half-plane  H = {z ∈ C:  Im(z) > 0}  is called a weak Maass form...

bracket when considering a ring of modular forms as a Lie algebra. Maass–Shimura operator Cohen, Henri (1975), "Sums involving the values at negative integers...

eigenvalues of Hecke operators on Siegel cusp forms of degree two", Invent. Math., 49 (2): 149–165, doi:10.1007/bf01403084, MR 0511188 Maass, Hans (1979a),...

conjecture for general linear groups over function fields. Maass wave form Harmonic Maass form Arthur's conjectures Arthur, James (1981), "The trace formula...

was the work of Michio Kuga with contributions also by Mikio Sato, Goro Shimura, and Yasutaka Ihara, followed by Deligne (1971). The existence of the connection...

action. Maass forms are real-analytic eigenfunctions of the Laplacian but need not be holomorphic. The holomorphic parts of certain weak Maass wave forms...

{X}}/\ln {X}} Selberg's 1/4 conjecture: the eigenvalues of the Laplace operator on Maass wave forms of congruence subgroups are at least 1 / 4 {\displaystyle...