The distribution of directions in an affine lattice: two-point correlations and mixed moments

混合特征中的几何萨塔克等价与斯宾纳对应

Geometric Satake equivalence in mixed characteristic and Springer correspondence

本文研究了混合特征中几何萨塔克等价与斯宾纳对应的联系，通过构造单向结构和同构，证明了在足够分枝条件下两者的关系。

Satake范畴上的两种monoidal结构

Two monoidal structures on Satake category in mixed characteristic

本文解释了两种几何Satake等价性的重合，包括Satake范畴上两种对称monoidal结构的重合。

Mixed moments of the Riemann zeta function

We analyse a collection of mixed moments of the Riemann zeta function and establish the validity of asymptotic formulae. Such examinations are performed both unconditionally and under the assumption of a weaker version of the $abc$ conjecture.

素数导体二次狄利克雷L函数的混合二阶矩

The Mixed Second Moment of Quadratic Dirichlet $L$-functions with Prime Conductors

本文在函数域语境下，针对首一不可约多项式平均的情况，建立了含完备L函数二阶导数的混合二阶矩的渐近公式。

函数域上素二次Dirichlet L-函数的混合二阶矩

The mixed second moment of prime quadratic Dirichlet $L$-functions over function fields

该研究在函数域背景下，针对首一不可约多项式对应的二次Dirichlet L-函数的μ阶和ν阶导数，计算出其混合二阶矩的渐近公式，为相关L-函数导数矩的研究提供了结果。

Hecke特征形式与L-函数混合矩的混合矩

Mixed moments of Hecke eigenforms and $L$-functions

研究Hecke特征形式不同重量的混合(2,2)矩的期望和方差估计，应用于三重积L-函数，基于L-函数的矩证明。

Twisted mixed moments of the Riemann zeta function

We analyse a collection of twisted mixed moments of the Riemann zeta function and establish the validity of asymptotic formulae comprising on some instances secondary terms of the shape $P(\log T) T^{C}$ for a suitable constant $C<1$ and a polynomial $P(x)$. Such examinations are performed both unconditionally and under the assumption of a weaker version of the $abc$-conjecture.

Hecke L-函数与黎曼ζ函数的混合积分矩

Mixed integral moments of the Hecke $L$-functions and Riemann zeta function

本文研究了Hecke L-函数与黎曼ζ函数在临界线上的混合矩，并建立了适用于解析形式和Maass形式的渐近公式。

自守形式的混合四阶矩与 $L$-函数的移位矩

Mixed fourth moments of automorphic forms and the shifted moments of $L$-functions

本文在GRH和GRC假设下，研究自守形式与Eisentein级数的混合四阶矩，揭示非均匀分布现象并提出相关猜想。

关于 L-函数混合矩中的误差项

On the error term in a mixed moment of L-functions

本文研究了 Dirichlet L-函数第四矩及被 Dirichlet 特征扭曲的自守 L-函数混合矩渐近式中的误差项优化问题，并成功改进了后者的误差项。

GL(2) 与对称平方 L 函数的混合矩

Mixed moments of $\rm GL(2)$ and symmetric square $L$-functions

该研究推导短区间内 GL(2) 及其对称平方 L 函数混合矩的渐近公式，并据此定量证明两类自守形式对应 L 函数中心值的同时非零性。

混合导数的黎曼ζ函数离散二次矩

The discrete second moment of mixed derivatives of the Riemann zeta function

本文研究了黎曼ζ函数在ζ零点处混合导数的离散二次矩的渐进行为，扩展了Conrey--Snaith和Milinovich的工作，提供了无条件和有条件误差项。

Mixed moment of $GL(2)$ and $GL(3)$ $L$-functions

Let $ \mathfrak{f} $ run over the space $ H_{4k} $ of primitive cusp forms of level one and weight $ 4k $, $ k \in N $. We prove an explicit formula for the mixed moment of the Hecke $ L $-function $ L(\mathfrak{f}, 1/2) $ and the symmetric square $L$-function $ L(sym^2\mathfrak{f}, 1/2)$, relating it to the dual mixed moment of the double Dirichlet series and the Riemann zeta function weighted by the ${}_3F_{2}$ hypergeometric function. Analysing the corresponding special functions by the means of the Liouville-Green approximation followed by the saddle point method, we prove that the initial…

扭曲混合 $L$-函数的混合矩

Mixed moments of twisted $L$-functions

本文研究了狄利克雷 $L$-函数和自守 $L$-函数在所有原始特征下的扭曲混合矩，推导出具有最优误差项的渐近公式，扩展了先前关于素数模数的研究结果。

Mixed moments of characteristic polynomials of random unitary matrices

Following the work of Conrey, Rubinstein and Snaith and Forrester and Witte we examine a mixed moment of the characteristic polynomial and its derivative for matrices from the unitary group U(N) (also known as the CUE) and relate the moment to the solution of a Painleve differential equation. We also calculate a simple form for the asymptotic behaviour of moments of logarithmic derivatives of these characteristic polynomials evaluated near the unit circle.