Ratios of Artin L-functions

Hochfilzer, Leonhard; Oliver, Thomas

Abstract

We study the cancellation of zeros between the Riemann zeta function and certain Artin L-functions. To do so, we develop 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.

Citation

Hochfilzer, L., & Oliver, T. (2022). Ratios of Artin L-functions. Journal of Number Theory, 236, 1-40. https://doi.org/10.1016/j.jnt.2021.07.007

• Journal Article Type: Article
• Acceptance Date: Jul 30, 2021
• Online Publication Date: Aug 26, 2021
• Publication Date: Jul 1, 2022
• Deposit Date: Nov 18, 2021
• Publicly Available Date: Aug 27, 2023
• Journal: Journal of Number Theory
• Print ISSN: 0022-314X
• Electronic ISSN: 1096-1658
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 236
• Pages: 1-40
• DOI: https://doi.org/10.1016/j.jnt.2021.07.007
• Keywords: Algebra and Number Theory
• Public URL: https://nottingham-repository.worktribe.com/output/6054980
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0022314X21002626
• Additional Information: This article is maintained by: Elsevier; Article Title: Ratios of Artin L-functions; Journal Title: Journal of Number Theory; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.jnt.2021.07.007