论文标题
Dedekind Zeta值1/2的注释
A note on Dedekind zeta values at 1/2
论文作者
论文摘要
对于一个数字字段$ k $，令$ζ_{k}（s）$是与$ k $相关的dedekind zeta函数。在本说明中，我们研究了$ζ_{k} $的非泛滥和超越性，以及其导数$ζ_{k}'$ at $ s = 1/2 $。在途中，我们加强了Ram Murty和Tanabe证明的结果[关于$ e^γ$的性质以及$ l $ series的不变，$ s = 1/2 $，J。数字理论161（2016）444-456]。
For a number field $K$, let $ζ_{K}(s)$ be the Dedekind zeta function associated to $K$. In this note, we study non-vanishing and transcendence of $ζ_{K}$ as well as its derivative $ζ_{K}'$ at $s= 1/2$. En route, we strengthen a result proved by Ram Murty and Tanabe [On the nature of $e^γ$ and non-vanishing of $L$-series at $s= 1/2$, J. Number Theory 161 (2016) 444-456].
