论文标题
正方形和多个Dirichlet系列的算术进程
Arithmetic Progressions of Squares and Multiple Dirichlet Series
论文作者
论文摘要
我们研究了两个变量的Dirichlet系列，该序列计算了正方形的原始三项算术进程。我们表明，这个多个Dirichlet系列具有Meromormorphic延续至$ \ Mathbb {C}^2 $，并使用Tauberian方法获得了正方形和合理点的算术进程的计数，$ x^2+y^2 = 2 = 2 $。
We study a Dirichlet series in two variables which counts primitive three-term arithmetic progressions of squares. We show that this multiple Dirichlet series has meromorphic continuation to $\mathbb{C}^2$ and use Tauberian methods to obtain counts for arithmetic progressions of squares and rational points on $x^2+y^2=2$.
