On the mean square of an arithmetical error term of the Selberg class in short intervals
On the mean square of an arithmetical error term of the Selberg class in short intervals
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DOI：
10.1142/s1793042116501037
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发表时间：
2016-07
影响因子：
0.7
通讯作者：
Xiaodong Cao;Y. Tanigawa;W. Zhai
中科院分区：
文献类型：
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作者：
Xiaodong Cao;Y. Tanigawa;W. Zhai
设∑n=1∞a(N)n−S是d次Selberg型狄里克莱级数，E(X)是∑n≤xa(N)的算术误差项。我们得到了Jutila型短区间上E(X)的两种均方估计。我们的方法是基于E(X)的截断型公式。我们还给出了这些估计在算术问题中的几个应用。
Let ∑n=1∞a(n)n−s be a Dirichlet series in the Selberg class of degree d and let E(x) be the arithmetical error term of ∑n≤xa(n). We derive two kinds of the mean square estimates of E(x) in short intervals of Jutila’s type. Our method is based on the truncated Tong-type formula of E(x). We also give several applications of these estimates in the arithmetical problems.