论文标题
在Zeta函数的诺斯科特属性上
On the Northcott property of zeta functions over function fields
论文作者
论文摘要
Pazuki和Pengo定义了诺斯科特（Northcott）的属性，用于特殊的数字字段Zeta功能和某些动机$ L $ functions的特殊值。我们确定Northcott属性在函数字段上具有恒定字段$ \ mathbb {f} _q $外部的值。 We then use a case by case approach for some values inside the critical strip, notably $Re (s) < \frac{1}{2} - \frac{\log 2}{\log q}$ and for $s$ real such that $1/2 \leq s \leq 1$, and we obtain a partial result for complex $s$ in the case $1/2< Re(s)\leq 1$ using recent advances在移动的矩上，猜想在功能场上。
Pazuki and Pengo defined a Northcott property for special values of zeta functions of number fields and certain motivic $L$-functions. We determine the values for which the Northcott property holds over function fields with constant field $\mathbb{F}_q$ outside the critical strip. We then use a case by case approach for some values inside the critical strip, notably $Re (s) < \frac{1}{2} - \frac{\log 2}{\log q}$ and for $s$ real such that $1/2 \leq s \leq 1$, and we obtain a partial result for complex $s$ in the case $1/2< Re(s)\leq 1$ using recent advances on the Shifted Moments Conjecture over function fields.
