Schanuel's conjecture and the exceptional set of $γ$-th arithmetic zeta functions

广义多重 Hurwitz zeta 函数在非正整数处的值与导数值

Values and derivative values at nonpositive integers of generalized multiple Hurwitz zeta functions

本文建立广义 Hurwitz 型多重 zeta 函数的亚纯延拓，导出其沿给定方向在非正整数处的值及导数值公式，并应用于 Witten zeta 函数与 $\mathfrak{g}_2$ 表示数的渐近分析。

Elementary methods in the study of Deuring-Heilbronn Phenomenon

The aim of this work is to improve some elementary results regarding both the Deuring-Phenomenon and the Heilbronn-Phenomenon. We will give better estimates regarding both the influence of zeros of the Riemann zeta function on the exceptional zeros and that of the non-trivial zeros of arbitrary L-functions belonging to non-principal characters on the exceptional zeros.

Critical zeros of lacunary L-functions

Assuming the existence of a sequence of exceptional discriminants of quadratic fields, we show that a hundred percent of zeros of the Riemann zeta function are on the critical line in specific segments. This is a special case of a more general statement for lacunary $L$-functions.

多重zeta星值的归一化逼近函数

The normalized approximation function for multiple zeta-star values

该研究受拉格朗日谱及其连分数倒数形式启发，引入多重zeta星值的归一化逼近函数，证明其正则性、可测性等性质，得出几乎所有大于1的实数对应函数值为0且像集稠密的结论。

正则化多重正切函数与约化定理

Regularized Multitangent Functions and Reduction Theorem

该研究建立stuffle正则化多重正切函数的直接解析理论，通过渐近比较等方法证明其可约化为单正切函数的有限线性组合，并推导得到正则化多重zeta值间的一族关系式。

奇偶扰动的Hofstadter Q递归的双变量ζ函数：特殊的t=-1切片与高斯边界层

A Two-Variable Zeta Function for a Parity-Perturbed Hofstadter Q-Recursion: The Exceptional t = -1 Slice and Gaussian Boundary Layers

本文研究奇偶扰动的Hofstadter Q递归及其双变量狄利克雷级数，推导相关恒等式，得到t=-1切片的渐近结果与边界共振晶格，分析负偶拱通道的高斯极限与负拱质量的显式表达式。

Böttcher 坐标的双代数几何

Bialgebraic geometry of Böttcher coordinates

研究多项式 f 的 Böttcher 坐标 Ψ_f 下的双代数集，在 Julia 集不连通或连通且具有非退化局部连通模型时给出完全动力学分类，并证明类似 Ax-Lindemann-Weierstrass 定理的结论。

数域上费马曲面的伽罗瓦不变奈龙 - 塞维里秩：伽罗瓦模、封闭形式、阈值及精确表格

Galois-invariant Néron--Severi ranks of Fermat surfaces over number fields: a Galois module, closed forms, a threshold, and exact tables

研究数域上费马曲面的伽罗瓦不变奈龙 - 塞维里秩，通过显式特征平均计算，给出\(\gcd(d,6)=1\)时封闭形式及\(4\leq d\leq30\)的有理秩，证明相关公式，建立阈值和轨道规则，给出精确表格及平均阶，结果无条件且有辅助文件支持。

An effective Chebotarev density theorem for families of number fields, with an application to $\ell$-torsion in class groups

We prove a new effective Chebotarev density theorem for Galois extensions $L/\mathbb{Q}$ that allows one to count small primes (even as small as an arbitrarily small power of the discriminant of $L$); this theorem holds for the Galois closures of "almost all" number fields that lie in an appropriate family of field extensions. Previously, applying Chebotarev in such small ranges required assuming the Generalized Riemann Hypothesis. The error term in this new Chebotarev density theorem also avoids the effect of an exceptional zero of the Dedekind zeta function of $L$, without assuming GRH. We g…