论文标题
单个模量的算术进程中k折的函数的差异
Variance of the k-fold divisor function in arithmetic progressions for individual modulus
论文作者
论文摘要
在本文中，我们证实了最近在限制范围内，算术进程中k折的差异函数方差的近期猜想的平滑版本。与Rodgers和Soundararajan的先前结果相反，我们不需要在模量上平均。我们的证明适应了S. lester的技术，该技术在相同范围内处理了k折的分隔函数的方差，并以短时间的设置为基础，并基于平滑的voronoi求和公式，但由乘法字符扭曲。使用Dirichlet字符的使用使我们可以扩展到更广泛的范围，从使用加法字符的Kowalski和意大利乳清干酪的先前结果。平滑还可以使我们无条件地对待所有K。该结果与Dirichlet L功能的时刻密切相关。
In this paper, we confirm a smoothed version of a recent conjecture on the variance of the k-fold divisor function in arithmetic progressions to individual composite moduli, in a restricted range. In contrast to a previous result of Rodgers and Soundararajan, we do not require averaging over the moduli. Our proof adapts a technique of S. Lester who treated in the same range the variance of the k-fold divisor function in the short intervals setting, and is based on a smoothed Voronoi summation formula but twisted by multiplicative characters. The use of Dirichlet characters allows us to extend to a wider range from previous result of Kowalski and Ricotta who used additive characters. Smoothing also permits us to treat all k unconditionally. This result is closely related to moments of Dirichlet L-functions.
