ochiai/mock - PukiWiki
 ¡¡ modular form: (1) modularity, (2) holomorphic, (3) holomorphic at cusps. How they are generalized or restricted ? cusp form: (3) vanishes at cusps. non-holomoprhic modular form(?): (2) real analytic, and eigenfunction of Casimir operator. weakly holomorphic modular form: (3) allowing finite-order pole at cusps. harmonic Maass form: (2) real analytic, and annihilated by weight-$k$-Laplacian. (3) at most linear exponential growth at cusps. weak Maass form: (2) real analytic, and eigenfunction of weight-$k$-Laplacian. (3) at most linear exponential growth at cusps. mock modular form: holomorphic part'' of harmonic Maass form. meromorphic modular form: weakly holomorphic cusp form: weakly holomorphic, and its Fourier expansion has no $q^0$ terms. (still may allow $q^n$ with negative $n$.) quasi-modular form Generalization to another direction modular form with half integral weight Siegel modular form Jacobi form Notations $M_k$ modular form $S_k$ cusp form $M^!_k$ weakly holomorphic modular form $S^!_k$ weakly holomorphic cusp form $QM_k$ quasi-modular form

Last-modified: 2016-11-24 (ÌÚ) 15:11:20 (457d)