共轭类中的双曲格点问题
The hyperbolic lattice point problem in conjugacy classes
摘要：
对于$Γ$（上紧或上有限富克斯群），我们研究了共轭类中的双曲格点问题，它是经典双曲格点问题的一个改进.我们使用大筛不等式的黎曼曲面$Γ\backslash \mathbb H$，以获得平均结果的误差项，这是最佳的。本文给出了A.好.对于$\hbox{SL}(2,{\mathbb Z})$，我们解释我们的结果在不定二次型。
英文摘要：
For $Γ$ a cocompact or cofinite Fuchsian group, we study the hyperbolic lattice point problem in conjugacy classes, which is a modification of the classical hyperbolic lattice point problem. We use large sieve inequalities for the Riemann surfaces $Γ\backslash \mathbb H$ to obtain average results for the error term, which are conjecturally optimal. We give a new proof of the error bound $O(X^{2/3})$, due to A. Good. For $\hbox{SL}(2,{\mathbb Z})$ we interpret our results in terms of indefinite quadratic forms.
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