模形式周期多项式的黎曼假设
数论
2016-04-27 v3
摘要
对于偶权重新形式，其周期多项式是临界值的生成函数。它有一个函数方程将与联系起来。我们证明了这些多项式的黎曼假设：即的零点位于圆上。我们证明了当或较大时，这些零点是等分布的。
引用
@article{arxiv.1601.03114,
title = {The Riemann Hypothesis For Period Polynomials Of Modular Forms},
author = {Seokho Jin and Wenjun Ma and Ken Ono and Kannan Soundararajan},
journal= {arXiv preprint arXiv:1601.03114},
year = {2016}
}
备注
11 pages. We added the one sentence explanation for the $2n^{(k-1)/2}$ bound for $\Lambda_f(n)$. This paper will be appearing in Proceedings of the National Academy of Sciences, USA