论文标题
L功能矩的渐近学中的次要术语
Secondary terms in the asymptotics of moments of L-functions
论文作者
论文摘要
我们为现有的猜想渐近公式提出了一个精致的版本，以在有理功能领域的二次dirichlet l功能范围内的瞬间。我们的预测是由两个自然猜想提供的，它们提供了足够的信息，以确定分析性能（Meromororphic延续，杆的位置和每个极点在每个极点）的某种二次L功能矩的生成功能。我们的渐近公式的数字字段类似物可以通过类似的程序获得，唯一的区别是来自阿基米德人甚至地方的贡献，需要单独分析。为了避免此其他技术问题，为简单起见，我们仅在理性函数字段设置中介绍了渐近公式。这也具有更容易测试的优点。
We propose a refined version of the existing conjectural asymptotic formula for the moments of the family of quadratic Dirichlet L-functions over rational function fields. Our prediction is motivated by two natural conjectures that provide sufficient information to determine the analytic properties (meromorphic continuation, location of poles, and the residue at each pole) of a certain generating function of moments of quadratic L-functions. The number field analogue of our asymptotic formula can be obtained by a similar procedure, the only difference being the contributions coming from the archimedean and even places, which require a separate analysis. To avoid this additional technical issue, we present, for simplicity, the asymptotic formula only in the rational function field setting. This has also the advantage of being much easier to test.
