Formal degrees and the local theta correspondence: the quaternionic case

刚性内扭曲的局部theta对应与朗兰兹参数

Local theta correspondences and Langlands parameters for rigid inner twists

本文提出用刚性内扭曲的局部朗兰兹对应描述局部theta对应（含四元数对偶对对应）的猜想，并验证其在特定情况下成立。

The non-tempered theta 10 Arthur parameter and Gross-Prasad Conjectures

We provide a construction of local and automorphic non-tempered Arthur packets of the group SO(3,2) and its inner form SO(4,1) associated with a certain Arthur's parameter and prove a multiplicity formula. We further study the restriction of the representations in these packets to the subgroup SO(3,1). In particular, we discover that the local Gross-Prasad conjecture, formulated for generic L-packets, does not generalize naively to a non-generic A-packet. We also study the non-vanishing of the automorphic SO(3,1)-period on the group SO(4,1) x SO(3,1) and SO(3,2) x SO(3,1) for the representatio…

The leading root of the partial theta function

I study the leading root x_0(y) of the partial theta function Θ_0(x,y) = \sum_{n=0}^\infty x^n y^{n(n-1)/2}, considered as a formal power series. I prove that all the coefficients of -x_0(y) are strictly positive. Indeed, I prove the stronger results that all the coefficients of -1/x_0(y) after the constant term 1 are strictly negative, and all the coefficients of 1/x_0(y)^2 after the constant term 1 are strictly negative except for the vanishing coefficient of y^3.

有限傅里叶对偶、径向值与一个模八假 theta 商式的算术

Finite Fourier Duality, Radial Values, and Arithmetic of a Mod Eight False Theta Quotient

研究模八假 theta 矩商式的径向行为，建立有限傅里叶闭包，证明周期狄利克雷值非零，并给出系数整除性、二进插值及欧拉变换正性等算术结果。

等秩局部theta对应作为强Morita等价

Equal rank local theta correspondence as a strong Morita equivalence

本文证明等秩约化对偶对的theta对应双射可由两个C*-代数表示范畴间的Morita等价实现，并由此推出双射的函子性、连续性及特征标与形式度的相关性质。