Bias of Root Numbers for Hilbert Newforms of Cubic Level
Number Theory
2022-05-31 v2
Abstract
We give a general formula of the bias of root numbers for Hilbert modular newforms of cubic level. Explicit calculation is given when the base field is and the level is the cube of certain rational integers. This complements a previous result of the second author and extends the bias phenomenon to the number fields. Our method is based on Jacquet-Zagier's trace formula, and the explicit calculation works generally for all real quadratic fields of narrow class number one and for rational cubic levels.
Keywords
Cite
@article{arxiv.2110.08310,
title = {Bias of Root Numbers for Hilbert Newforms of Cubic Level},
author = {Zhilin Luo and Qinghua Pi and Han Wu},
journal= {arXiv preprint arXiv:2110.08310},
year = {2022}
}