Ratios of Artin L-functions
Number Theory
2023-07-14 v5
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.
Keywords
Cite
@article{arxiv.1910.02821,
title = {Ratios of Artin L-functions},
author = {Leonhard Hochfilzer and Thomas Oliver},
journal= {arXiv preprint arXiv:1910.02821},
year = {2023}
}
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35 pages