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arXiv · 1910.02821

Ratios of Artin L-functions

Leonhard Hochfilzer·Thomas Oliver
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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.

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Leonhard Hochfilzer, Thomas Oliver. 2019-10-07. Ratios of Artin L-functions. https://doi.org/10.1016/j.jnt.2021.07.007

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