Continuous lower bounds for moments of the mixed product of twisted L-functions

Abstract

Let $f_1,f_2$ be two distinct cuspidal holomorphic Hecke eigenforms of even weight ${\kappa }_1,{\kappa }_2$ for the modular group $S{L}_2\left(Z\right)$ respectively. Let $L(s,f_1\otimes \chi ),L(s,f_2\otimes \chi )$ denote twisted L-functions associated to $f_1,f_2$ twisted by a primitive Dirichlet character χ modulo q respectively. In this paper, we obtain sharp lower bounds for all positive real k-th $(k>1)$ moments of the mixed product of these two twisted L-functions at the central value, which extend the previous results.