论文标题
使用双Dirichlet系列的真实字符的平均值
Mean value of real characters using a double Dirichlet series
论文作者
论文摘要
我们研究双字符$ $ \ sum \ limits _ {\ ordack {m \ leq x，\\ m \ odd}}} \ sum \ sum \ limits _ {\ setack {n \ leq y，\ leq y，\\ n \ odd}}}} \ leg n $ and and and and and and and and Flower towerplowed and and and and and and Flowed Towned unterpart。 Conrey，Farmer和Soundararajan通过应用Poisson求和公式获得了带有节能错误术语的渐近公式。结果很有趣，因为主要术语涉及非平滑函数。在本文中，我们应用了两次逆变蛋白转换，并研究了涉及双dirichlet系列的结果双积分。该方法具有两个优点 - 它导致了一个更好的错误项，而令人惊讶的主术语自然源自双dirichlet系列的三个残基。
We study the double character sum $\sum\limits_{\substack{m\leq X,\\m\odd}}\sum\limits_{\substack{n\leq Y,\\n\odd}}\leg mn$ and its smoothly weighted counterpart. An asymptotic formula with power saving error term was obtained by Conrey, Farmer and Soundararajan by applying the Poisson summation formula. The result is interesting, because the main term involves a non-smooth function. In this paper, we apply the inverse Mellin transform twice and study the resulting double integral that involves a double Dirichlet series. This method has two advantages -- it leads to a better error term, and the surprising main term naturally arises from three residues of the double Dirichlet series.
