Period functions for vector-valued Maass cusp forms of real weight, with
an application to Jacobi Maass cusp forms
Period functions for vector-valued Maass cusp forms of real weight, with
an application to Jacobi Maass cusp forms
For vector-valued Maass cusp forms for~$SL_2(\mathbb{Z})$ with real weight~$k\in\mathbb{R}$ and spectral parameter $s\in\mathbb{C}$, $\mathrm{Re} s\in (0,1)$, $s\not\equiv \pm k/2$ mod $1$, we propose a notion of vector-valued period functions, and we establish a linear isomorphism between the spaces of Maass cusp forms and period functions by means of a cohomological …