The Ratios Conjecture and upper bounds for negative moments of ?-functions over function fields
The Ratios Conjecture and upper bounds for negative moments of ?-functions over function fields
复制标题
函数域上 ?-函数负矩的比率猜想和上限
DOI：
10.1090/tran/8907
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发表时间：
2023
影响因子：
1.3
通讯作者：
Keating, Jonathan
中科院分区：
文献类型：
--
作者：
Bui, Hung;Florea, Alexandra;Keating, Jonathan
证明了函数域上二次狄利克雷函数族的比率猜想的特殊情形。更具体地说，我们研究的平均值，当在monic，平方自由多项式的degreeover，作为，我们得到一个渐近公式时。本文还研究了重叠函数乘积的平均值，得到了当分母的位移的真实的部分分别大于和时的渐近公式。证明中的主要内容是得到函数负矩的上界。我们得到的上界预计在上述范围内几乎是尖锐的。引用
We prove special cases of the Ratios Conjecture for the family of quadratic Dirichlet-functions over function fields. More specifically, we study the average of, whenvaries over monic, square-free polynomials of degreeover, as, and we obtain an asymptotic formula when. We also study averages of products ofoverandover-functions, and obtain asymptotic formulas when the shifts in the denominator have real part bigger thanandrespectively. The main ingredient in the proof is obtaining upper bounds for negative moments of-functions. The upper bounds we obtain are expected to be almost sharp in the ranges described above. References