论文标题
确切的扭曲L值的双重平均值
Exact double averages of twisted L-values
论文作者
论文摘要
考虑中央$ l $ l $ - 重量椭圆形或希尔伯特模块化表格$ f $ twist twist twist twist twist twist twist twist twist，由理想的类字符$χ$ themiminary二次扩展$ k $。固定$χ$，假设$ k $在每个质量上都惰性，将平均值的简单确切配方划分为平均$ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $。当相对于$ k $（“稳定范围”）的水平较大时，这些平均值会稳定。 在重量2中，我们获得了超过$ f $和$χ$的同时平均值的精确公式。我们允许使用任何数量的主要因素，并将$ k $超过水平分配。在基本条件下，这些双重平均值在所有范围内都是“稳定”的。两个后果是对上述稳定（单个）平均值的概括，并且对中央$ l $价值的不断变化有效。
Consider central $L$-values of even weight elliptic or Hilbert modular forms $f$ twisted by ideal class characters $χ$ of an imaginary quadratic extension $K$. Fixing $χ$, and assuming $K$ is inert at each prime dividing the level, one knows simple exact formulas for averages over newforms $f$ of squarefree levels satisfying a parity condition on the number of prime factors. These averages stabilize when the level is large with respect to $K$ (the "stable range"). In weight 2, we obtain exact formulas for a simultaneous average over both $f$ and $χ$. We allow for non-squarefree levels with any number of prime factors, and ramification or splitting of $K$ above the level. Under elementary conditions on the level, these double averages are "stable" in all ranges. Two consequences are generalizations of the aforementioned stable (single) averages and effective results on nonvanishing of central $L$-values.
