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arXiv · 2110.08310

Bias of Root Numbers for Hilbert Newforms of Cubic Level

Zhilin Luo·Qinghua Pi·Han Wu
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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 $\mathbb{Q}, \mathbb{Q}(\sqrt{2}), \mathbb{Q}(\sqrt{5})$ 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.

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Zhilin Luo, Qinghua Pi, Han Wu. 2021-10-15. Bias of Root Numbers for Hilbert Newforms of Cubic Level. https://arxiv.org/abs/2110.08310

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