A Variation on the Solvable Case of the Dedekind Conjecture

LetGbe the Galois group of a solvable Galois extension K/F of number fields. In this note, we demonstrate the holomorphy of certain Artin L-functions attached to K/F, generalizing results of M. R. Murty and A. Raghuram [1]. We also give a bound (generalizing one in [1]) on the orders of certain Artin L-functions at an arbitrary point in the complex plane by the order of a corresponding quotient of Dedekind zeta functions. We deduce some corollaries on the possible orders of zeros of such quotients.