67 citations · 98 across the 20 of their papers we have counts for
21 papers
Stevens' Approach to Kloosterman Sums on Split Groups
Li Cai, Haoran Liu, Mingyu Yang +1
We develop a uniform framework for Stevens' approach to Kloosterman sums on split groups over -adic fields. The main result reduces the bounding of Kloosterman sums to that for…
Bessel Distributions and Kloosterman Sums
Li Cai, Jingsong Chai, Yadi Liu
Let be a split reductive group over a -adic field. We give germ expansions of Kloosterman integrals for . As an application, we prove that Bessel distributions are regula…
From n-systems to Lie and Courant algebroids
Liqiang Cai, Zhuo Chen, Zhixiong Chen +1
This paper introduces a method for constructing pure algebroids, dull algebroids, and Lie algebroids. The construction relies on what we deffned as n-systems on vector bundles, and…
Distributions of Integral Points and Dedekind Zeta Values
Li Cai, Taiwang Deng
Let be the ring of integers for some number field . Let be a regular monic polynomial of degree . We study the asymptotic count of inte…
On twisting functions
Li Cai
In this work, we unify different constructions of Kan's loop group for a reduced simplicial set topologically, by identifying its geometric realization as different…
On the graph products of simplicial groups and connected Hopf algebras
Li Cai
In this paper we study the classifying spaces of graph products of simplicial groups and connected Hopf algebras over a field, and show that they can be uniformly treated under the…
Spherical Characters in Families: the unitary Gan-Gross-Prasad case
Li Cai, Yangyu Fan
We consider the variation of spherical characters in families. We formulate conjectures for the rationality and meromorphic property of spherical characters. As an example, we esta…
Multiplicities of Representations in Algebraic Families
Li Cai, Yangyu Fan
In this short notes, we consider multiplicities of representations in general algebraic families, especially the upper semi-continuity of homological multiplicities and the locally…
Higher Ext-groups in the triple product case
Li Cai, Yangyu Fan
In this short note, we compute higher extension groups for all irreducible representations and deduce the multiplicity formula for finite length representations in triple product c…
Higher Ext-groups and Relatively Supercuspidal Spectra
Li Cai, Yangyu Fan
Relatively supercuspidal representations are analogue of supercuspidal representations in the relative Langlands program. This work studies relatively supercuspidal representations…
Families of Canonical Local Periods on Spherical Varieties
Li Cai, Yangyu Fan
We consider the variation of canonical local periods on spherical varieties proposed by Sakellaridis-Venkatesh in families. We formulate conjectures for the rationality and meromor…
Isolation of the Cuspidal Spectrum: the Function Field Case
Li Cai, Bin Xu
Isolating cuspidal automorphic representations from the whole automorphic spectrum is a basic problem in the trace formula approach. For example, matrix coefficients of supercupida…
On the KO-groups of toric manifolds
Li Cai, Suyoung Choi, Hanchul Park
In this paper we consider the real topological K-groups of a toric manifold M, which turns out to be closely related to the topology of the small cover MR, the fixed points under t…
On the 2-part of the Birch and Swinnerton-Dyer conjecture for quadratic twists of elliptic curves
Li Cai, Chao Li, Shuai Zhai
In the present paper, we prove, for a large class of elliptic curves defined over , the existence of an explicit infinite family of quadratic twists with analytic rank…
Integral cohomology groups of real toric manifolds and small covers
Li Cai, Suyoung Choi
For a simplicial complex with vertices, there is a canonical -space known as a real moment angle complex . In this paper, we consider…
Heegner Points on Modular Curves
Li Cai, Yihua Chen, Yu Liu
In this paper, we study the Heegner points on more general modular curves other than , which generalizes Gross' work "Heegner points on ". The explicit Gross-Zagier…
Cube Sum Problem and an Explicit Gross-Zagier Formula
Li Cai, Jie Shu, Ye Tian
A nonzero rational number is called a cube sum if it is of form with . In this paper, we prove that for any odd integer , there exist i…
On products in a real moment-angle manifold
Li Cai
In this paper we give a necessary and sufficient condition for a (real) moment-angle complex to be a topological manifold. The cup and cap products in a real moment-angle manifold…
Explicit Gross-Zagier and Waldspurger Formulae
Li Cai, Jie Shu, Ye Tian
We give an explicit form of Gross-Zagier formula on Shimura Curves and an explicit form of Waldspurger formula.
Norm minima in certain Siegel leaves
Li Cai
In this paper we shall illustrate that each polytopal moment-angle complex can be understood as the intersection of the minima of corresponding Siegel leaves and the unit sphere, w…
On the cohomology of polyhedral products with space pairs
Li Cai
In this note we prove that the integer cohomology ring of polyhedral products with space pairs can also be described explicitly by a multiplicative Hochster's formula.