论文标题
在ABC下的某些代数群体中分布非妻子的素数
Distribution of Non-Wieferich primes in certain algebraic groups under ABC
论文作者
论文摘要
在美国广播公司（ABC）的领导下，西尔弗曼（Silverman）表明，关于任何（非平凡的）基础$ a $，有无限的非威弗里希素数。最近，Srinivas和Subramani证明了与小组组相比的数字字段类似的结果。在本文的第一部分中，我们将其结果扩展到任何任意数字字段。其次，我们为非妻子素数理想的数量提供了渐近下限。此外，我们显示的是相同订单的下限，对于具有$ 1 \ pmodk。$符合$ 1 \ pmodk。$的非威弗里奇素数的下限是可以实现的，我们在Kühn和Müller待遇后，我们将Silverman的工作概括为椭圆曲线的工作。
Under ABC, Silverman showed that there are infinitely many non-Wieferich primes with respect to any (non-trivial) base $a$. Recently Srinivas and Subramani proved an analogous result over number fields with trivial class group. In the first part of this article, we extend their result to any arbitrary number fields. Secondly, we give an asymptotic lower bound for the number of non-Wieferich prime ideals. Furthermore, we show a lower bound of same order is achievable for non-Wieferich prime ideals having norm congruent to $1 \pmod k.$ Lastly, we generalize Silverman's work for elliptic curves over arbitrary number fields following the treatment by Kühn and Müller.
