论文标题
关于兰金 - 塞尔伯格问题
On the Rankin--Selberg problem
论文作者
论文摘要
在本文中，我们解决了兰金 - 塞尔伯格问题。也就是说，我们打破了众所周知的兰金 - 塞尔伯格（Selberg）的界限，这是$ \ mathrm {gl}（2）$ cusp形式的第二次傅立叶系数的错误术语（holomorthic and Maass），这是自从出生以来的80多年以来的记录。我们扩展了处理L功能系数平均值的方法，该系数可以分解为学位的乘积和三个L功能。
In this paper, we solve the Rankin--Selberg problem. That is, we break the well known Rankin--Selberg's bound on the error term of the second moment of Fourier coefficients of a $\mathrm{GL}(2)$ cusp form (both holomorphic and Maass), which remains its record since its birth for more than 80 years. We extend our method to deal with averages of coefficients of L-functions which can be factorized as a product of a degree one and a degree three L-functions.
