L-series for vector-valued modular forms

Motivated by the recent works of Bringmann, Guerzhoy, Kent, and Ono [4] and Bringmann, Fricke, and Kent [3], we introduce L-series for vector-valued weakly holomorphic cusp forms, and mock modular period polynomials for vector-valued harmonic weak Maass forms. In particular, we will discuss an integral representation of this new L-series and the limiting behavior of special values. Moreover, we also give relations between mock modular periods and L-series for vector-valued harmonic weak Maass forms.