Lower Bounds for Higher Moments of the Twisted L-functions

Abstract

Let f be a cuspidal holomorphic or Maass Hecke eigenform for the modular group $$\text{SL}_{2}(\mathbb{Z})$$ . Let $$L(s,f\otimes\chi)$$ denote the twisted L-function associated to f twisted by a primitive Dirichlet character χ modulo q. In this paper, we obtain a lower bound for the 2kth moment of central values of the twisted L-functions.