Ratios of Artin L-functions
arXiv:1910.02821 · doi:10.1016/j.jnt.2021.07.007
Abstract
We show that certain quotients of Artin L-functions have infinitely many poles. Our result follows from a converse theorem for Maass forms of Laplace eigenvalue 1/4 in which the twisted L-functions are not assumed to be entire. We do not require the conjectural automorphy of Artin L-functions, only their established meromorphic continuation and functional equation.
35 pages