Moments of Dirichlet L-functions with prime conductors over function fields
Moments of Dirichlet L-functions with prime conductors over function fields
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DOI：
10.1016/j.ffa.2020.101659
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发表时间：
2019-09
期刊：
影响因子：
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通讯作者：
H. Bui;Alexandra Florea
中科院分区：
文献类型：
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作者：
H. Bui;Alexandra Florea
当判别式的次数趋于无穷大时，我们计算 F q [x] 上具有素导体的二次狄利克雷 L 函数族中的二阶矩，获得低阶项之一。我们还获得了一个渐近公式，其前导项为与 F q (t) 上的固定椭圆曲线通过一元不可约多项式的二次扭曲相关的 L 函数导数的平均值。作为推论，我们证明存在无限多个一元不可约多项式，使得相应扭曲椭圆曲线的解析秩等于 1。
We compute the second moment in the family of quadratic Dirichlet L–functions with prime conductors over F q [x] when the degree of the discriminant goes to infinity, obtaining one of the lower order terms. We also obtain an asymptotic formula with the leading order term for the mean value of the derivatives of L–functions associated to quadratic twists of a fixed elliptic curve over F q (t) by monic irreducible polynomials. As a corollary, we prove that there are infinitely many monic irreducible polynomials such that the analytic rank of the corresponding twisted elliptic curves is equal to 1.