Quadratic transformations and Guillera's formulae for $1/π^2$

调和和与二次调和和的闭式公式与渐近公式

Closed and asymptotic formulae for harmonic and quadratic harmonic sums

本研究提出大量调和和与二次调和和的相关成果，给出了现有文献未记载的闭式公式，可应用于概率等实际问题。

A class of series acceleration formulae for Catalan's constant

In this note, we develop transformation formulae and expansions for the log tangent integral, which are then used to derive series acceleration formulae for certain values of Dirichlet L-functions, such as Catalan's constant. The formulae are characterized by the presence of an infinite series whose general term consists of a linear recurrence damped by the central binomial coefficient and a certain quadratic polynomial. Typically, the series can be expressed in closed form as a rational linear combination of Catalan's constant and pi times the logarithm of an algebraic unit.

二次曲面的求和公式

Summation formulae for quadrics

本文证明偶数变量二次曲面零点集上无支集限制的 Poisson 求和公式，边界项由常数或相关较小二次曲面求和表示，并借助 Arthur 截断 theta 提升建立其与正交群表示及二次型解数估计的联系。

论某些 Gram 矩阵及其相关级数

On certain Gram matrices and their associated series

本文研究 Riemann 假设 Nyman–Beurling 重构中的 Gram 矩阵，推导其公式、相关级数的积分表示与互反关系，并分解相应二次型。