报告题目：A partial result towards the Chowla--Milnor conjecture
报告人：李佳
邀请人：李从辉
报告时间：2026年9月18日下午16:00-17:00
报告地点：西南交通大学犀浦校区3教X30425
摘要：The Chowla--Milnor conjecture predicts the linear independence of certain Hurwitz zeta values. In this paper, we prove that for any fixed integer $k \geqslant 2$, the dimension of the $\mathbb{Q}$-linear span of $\zeta(k,a/q)-(-1)^{k}\zeta(k,1-a/q)$ ($1 \leqslant a < q/2$, $\gcd(a,q)=1$) is at least $(c -o(1)) \cdot \log q$ as the positive integer $q \to +\infty$ for some absolute constant $c>0$. It is well known that $\zeta(k,a/q)+(-1)^{k}\zeta(k,1-a/q) \in \overline{\mathbb{Q}}\pi^k$, but much less is known previously for $\zeta(k,a/q)-(-1)^{k}\zeta(k,1-a/q)$. Our proof is similar to those of Ball--Rivoal (2001) and Zudilin (2002) concerning the linear independence of Riemann zeta values. However, we use a new type of rational functions to construct linear forms.
报告人介绍：李佳，现为中国科学院数学与系统所博士后，博士毕业于北京大学，导师田青春教授，研究领域为数论，具体为多重zeta值、周期、混合tate motive以及L-函数特殊值的无理性问题。