Infinitesimal characters in arithmetic families

$p$-进流形上 Weil 丛的算术方面

Arithmetic Aspects of Weil Bundles over $p$-Adic Manifolds

本文建立 $p$-进解析流形上 Weil 丛的系统理论，证明其继承典范解析结构，并给出提升定理、Galois 等变结构及与晶体上同调的比较同构，应用于 $p$-进模形式和椭圆曲线的无穷小形变研究。

Nearly holomorphic automorphic forms on Sp(2n) with sufficiently regular infinitesimal characters and applications

In this paper, we decompose the space of nearly holomorphic Hilbert-Siegel automorphic forms as representations of the adele group under certain assumptions. We also give an application for classical holomorphic Hilbert-Siegel modular forms. In particular, we show the surjectivity of the global Siegel operator for certain congruence subgroups with large weights.

$p$-adic Banach表示的Gelfand-Kirillov界：具有$\text{GL}_2$和四元单位的微小特征

Gelfand-Kirillov bound for $p$-adic Banach representations with infinitesimal character for $\text{GL}_2$ and quaternion units

本文研究了$p$-adic Banach表示的Gelfand-Kirillov界，针对$\text{GL}_2$和四元单位群，证明了具有微小特征的表示维度上限。

无穷小特征与Lafforgue伪特征

Infinitesimal characters and Lafforgue's pseudocharacters

本文推广已有构造，将无穷小特征与p-adic局部域伽罗瓦群的Lafforgue伪特征族关联，并用于研究万有包络代数中心在完全上同调Hecke特征空间局部解析向量上的作用。

A local trace formula for $p$-adic infinitesimal symmetric spaces: the case of Guo-Jacquet

We establish an invariant local trace formula for the tangent space of some symmetric spaces over a non-archimedean local field of characteristic zero. These symmetric spaces are studied in Guo-Jacquet trace formulae and our methods are inspired by works of Waldspurger and Arthur. Some other results are given during the proof including a noninvariant local trace formula, Howe's finiteness for weighted orbital integrals and the representability of the Fourier transform of weighted orbital integrals. These local results are prepared for the comparison of regular semi-simple terms, which are weig…

On Character Sums and Exponential Sums over Generalized Arithmetic Progressions

We study upper bounds for sums of Dirichlet characters. We prove a uniform upper bound of the character sum over all proper generalized arithmetic progressions, which generalizes the classical Polya and Vinogradov inequality. Our argument is based on getting an upper bound for the l1 norm of the Fourier coefficients of a generalized arithmetic progression. Our method also applies to give upper bounds for polynomial exponential sums.