论文标题
谐波maass形式的l值
L-values of harmonic Maass forms
论文作者
论文摘要
Bruinier，Funke和Imamoglu已证明了一个模块化$ J $ -INVARIANT的哲学上可以称为“中央$ l $ value”的公式。以前，这是Zagier提出的启发性。在这里，我们将此“ $ l $ - 价值”解释为实际$ l $ series的价值，并将其扩展到所有不可或缺的论点，并将其扩展到包括所有弱塑形尖端形式的大量谐波maass形式。讨论了与先前定义的$ l $ series的上下文和关系，用于弱塑形和谐波形式。这些公式建议在这些情况下$ l $值的算术或几何含义。证明的关键要素是应用Lee，Raji和作者的最新理论来描述使用测试功能的谐波Maass $ L $ functions。
Bruinier, Funke, and Imamoglu have proved a formula for what can philosophically be called the "central $L$-value" of the modular $j$-invariant. Previously, this had been heuristically suggested by Zagier. Here, we interpret this "$L$-value" as the value of an actual $L$-series, and extend it to all integral arguments and to a large class of harmonic Maass forms which includes all weakly holomorphic cusp forms. The context and relation to previously defined $L$-series for weakly holomorphic and harmonic Maass forms are discussed. These formulas suggest possible arithmetic or geometric meaning of $L$-values in these situations. The key ingredient of the proof is to apply a recent theory of Lee, Raji, and the authors to describe harmonic Maass $L$-functions using test functions.
