论文标题
地形新形式的根号偏差
Bias of Root Numbers for Modular Newforms of Cubic Level
论文作者
论文摘要
令$ h^{\ pm} _ {2k}（n^3）$表示立方级的模块化新形式$ n^3 $，权重$ 2 k $和根号$ \ pm 1 $。对于$ n> 1 $ squarefree和$ k> 1 $，我们使用一种分析方法来建立差额$ | h^{+} _ {2k}（n^3）| - | h^{ - } _ {2k}（n^3）| $作为$φ（n）$的乘积的倍数，$ \ mathbb {q}（\ sqrt { - n}）$的类数量。特别是，该公式对根号$+1 $表现出严格的偏见。我们的主要工具是用于此类新形式的根数简单的简单彼得森公式。
Let $H^{\pm}_{2k} (N^3)$ denote the set of modular newforms of cubic level $N^3$, weight $2 k$, and root number $\pm 1$. For $N > 1$ squarefree and $k>1$, we use an analytic method to establish neat and explicit formulas for the difference $|H^{+}_{2k} (N^3)| - |H^{-}_{2k} (N^3)|$ as a multiple of the product of $φ(N)$ and the class number of $\mathbb{Q}(\sqrt{- N})$. In particular, the formulas exhibit a strict bias towards the root number $+1$. Our main tool is a root-number weighted simple Petersson formula for such newforms.
