报告人：陈汉（德国哥廷根大学）

时 间：2024年6月25日10:00

地 点：海韵园数理大楼661

内容摘要:

H.W. Lenstra in 1979 introduced the notion of the Euclidean ideal class in order to generalize the concept of Euclidean domains and capture cyclic class groups. Recently, real biquadratic fields $K$ of the form $\Q(\sqrt{q}, \sqrt{kr})$ having a non-principal Euclidean ideal class were studied by some authors, under the condition $h_K=2$ and certain residue conditions and lower bound conditions regarding primes $q, k,$ and $r$. In this report, I will briefly introduce the previous research results on this issue, and show my latest research on this issue by demonstrating that the condition $h_K=2$ is enough in most cases, except when $q\equiv 1 \pmod 4$ and $k, r\equiv 3 \pmod 4$, to obtain the desired non-principal Euclidean class. I will present two proofs to establish the conclusion. The first one involves the explicit construction of the Hilbert class field of $K$. The second approach utilizes the properties of conductor in absolutely abelian extensions, along with the application of the Chebotarev density theorem.

个人简介：

陈汉，德国哥廷根大学博士，主要研究领域是数论，特别是丢番图方程、丢番图逼近和代数数论等方面，目前已经在Chinese Annals of Mathematics Series B上接受发表论文。

联系人：祝辉林