回路群的θ函数和算术导数

Analytic torsion of arithmetic quotients of the symmetric space SL(n,R)/SO(n)

In this paper we define a regularized version of the analytic torsion for arithmetic quotients of the symmetric space SL(n,R)/\SO(n). The definition is based on the study of the renormalized trace of the corresponding heat operators, which is defined as the geometric side of the Arthur trace formula applied to the heat operator

大θ

The big theta

该研究在数学表示论领域，证明了Howe大商能够通过在合适的代数上做张量积来得到，丰富了相关代数结构研究。

Approximation of $L^2$-analytic torsion for arithmetic quotients of the symmetric space $\mathrm{SL}(n,\mathbb{R})/\mathrm{SO}(n)$

In [MzM] we defined a regularized analytic torsion for quotients of the symmetric space $\mathrm{SL}(n,\mathbb{R})/\mathrm{SO}(n)$ by arithmetic lattices. In this paper we study the limiting behaviour of the analytic torsion as the lattices run through sequences of congruence subgroups of a fixed arithmetic subgroup. Our main result states that for principal congruence subgroups and strongly acyclic flat bundles, the logarithm of the analytic torsion, divided by the index of the subgroup, converges to the $L^2$-analytic torsion.

几何与算术 theta 对应

Geometric and arithmetic theta correspondences

本文以酉群为例介绍几何与算术 theta 对应，重点阐述 Kudla 纲领的最新进展及其应用。

关于推广Langlands-Shahidi方法求圈群的等差商

On Extending the Langlands-Shahidi Method to Arithmetic Quotients of Loop Groups

本文讨论了环群G^的算术乘积上的某些Eisenstein级数，它们与G^的极大抛物线相关的有限维群上的尖点形式有关。

SL（n，R）/ SO（n）算术乘积的谱渐近性

Spectral asymptotics for arithmetic quotients of SL(n,R)/SO(n)

本文研究了对称空间S=SL（n，R）/SO（n）中算术导数尖点谱的渐近分布.特别是，我们得到外尔定律的估计的剩余项。这将Duistermaat-Kolk-Varadarajan关于紧局部对称空间谱渐近性的结果推广到了非紧的情形。