We continue our study of GL_2 L-functions with the aim of providing upper bounds for their order of magnitude. As is familiar it suffices to provide such bounds on the critical line and, both for the sake of applications and for the ideas involved, we are most interested in breaking the convexity bound and this with respect to the conductor. In this paper we are interested primarily in L-functions attached to characters of the class group of the imaginary quadratic field K = Q((-D)~(1/2)). We are motivated by our paper [DFI4]. That work was not included in the current series because the class group L-functions are treated there directly. They may however be viewed as L-functions associated to cusp forms of weight 1, level D and character (the nebentypus) x_D(n) = ((-D)), (1,1) the Kronecker symbol (we assume throughout that -D is a fundamental discriminant).
展开▼
