Estermann zeta函数余切和的推广
Generalizations of a cotangent sum associated to the Estermann zeta function
摘要：
余切和与Estermann zeta函数的零点相关联。它们在黎曼假设的Nyman-Beurling判据中也被证明是重要的。本文的主要结果是证明了$\mathbb{R}$上存在唯一的正测度μ，且关于该测度μ，某些正规余切和是等分布的.改进以及进一步推广的渐近公式有关余切和。我们还证明了一个更一般的余切和的渐近公式以及余切和的时刻的渐近结果正在考虑。我们还给出了2k阶矩的增长率的估计，作为k的函数。
英文摘要：
Cotangent sums are associated to the zeros of the Estermann zeta function. They have also proven to be of importance in the Nyman-Beurling criterion for the Riemann Hypothesis. The main result of the paper is the proof of the existence of a unique positive measure μ on $\mathbb{R}$, with respect to which certain normalized cotangent sums are equidistributed. Improvements as well as further generalizations of asymptotic formulas regarding the relevant cotangent sums are obtained. We also prove an asymptotic formula for a more general cotangent sum as well as asymptotic results for the moments of the cotangent sums under consideration. We also give an estimate for the rate of growth of the moments of order 2k, as a function of k.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
