Subconvexity for a double Dirichlet series and non-vanishing of L-functions

We study a double Dirichlet series of the form Sigma(d) L(s, chi(d)chi)chi' (d)d(-w), where chi and chi' are quadratic Dirichlet characters with prime conductors N and M respectively. A functional equation group isomorphic to the dihedral group of order 6 continues the function meromorphically to C-2. The developed theory is used to prove an upper bound for the smallest positive integer d such that L(1/2, chi(dN)) does not vanish. Additionally, a convexity bound at the central point is established to be (MN)(3/8+epsilon) and a subconvexity bound of (MN(M + N))(1/)(6+epsilon) is proven. An application of bounds at the central point to the non-vanishing problem is also discussed.