论文标题
I型对二次dirichlet $ l $的一个和两个级别密度的贡献 - 功能字段的功能
Type-I contributions to the one and two level densities of quadratic Dirichlet $L$--functions over function fields
论文作者
论文摘要
使用比率猜想，我们写下一个具有较低顺序项的精确公式，其中一个二次dirichlet $ l $的零的两个级别密度 - 功能字段上的功能。我们将产生的各种术语表示为$ 0 $，I型和II型贡献。当对测试功能的傅立叶变换的支持受到足够限制时，我们严格地计算了类型$ 0 $和类型I项，并确认它们与猜想的答案匹配。当对支持的限制放松时，我们的结果表明，II型贡献在两个级别的密度中变得很重要。
Using the Ratios Conjecture, we write down precise formulas with lower order terms for the one and the two level densities of zeros of quadratic Dirichlet $L$--functions over function fields. We denote the various terms arising as Type-$0$, Type-I and Type-II contributions. When the support of the Fourier transform of the test function is sufficiently restricted, we rigorously compute the Type-$0$ and Type-I terms and confirm that they match the conjectured answer. When the restrictions on the support are relaxed, our results suggest that Type-II contributions become important in the two level density.
