$\mathcal{I}^\prime$-curvatures in higher dimensions and the Hirachi conjecture

$Q$-prime 曲率通过重整化特征形式的推广

Generalizations of the $Q$-prime curvature via renormalized characteristic forms

本文针对每个重整化特征形式推广了 CR 流形上的 $Q$-prime 曲率，证明其积分等于 Marugame 的全局 CR 不变量，并研究了相关的临界 CR GJMS 算子与 $P$-prime 算子的推广。

素数散射测地线定理

Prime scattering geodesic theorem

本文研究模曲面上散射测地线的分布与逗留时间，首次建立了散射测地线计数与素因子位于算术级数中的正整数之间的联系。

Nonlocal aspects of $λ$-symmetries and ODEs reduction

A reduction method of ODEs not possessing Lie point symmetries makes use of the so called $λ$-symmetries (C. Muriel and J. L. Romero, \emph{IMA J. Appl. Math.} \textbf{66}, 111-125, 2001). The notion of covering for an ODE $\mathcal{Y}$ is used here to recover $λ$-symmetries of $\mathcal{Y}$ as nonlocal symmetries. In this framework, by embedding $\mathcal{Y}$ into a suitable system $\mathcal{Y}^{\prime}$ determined by the function $λ$, any $λ$-symmetry of $\mathcal{Y}$ can be recovered by a local symmetry of $\mathcal{Y}^{\prime}$. As a consequence, the reduction method of Muriel and Romero f…

大亏格曲面的素数测地线定理与闭测地线

Prime geodesic theorem and closed geodesics for large genus

本文研究大亏格双曲曲面模空间中素数测地线定理的误差上界及其期望值，并利用所得结果证明长度显著小于√g的闭测地线大多简单且不可分离、长度显著大于√g的闭测地线大多非简单，从而证实Lipnowski-Wright猜想。