Alexander polynomials of knots and number theory

我们的研究目的是寻找拓扑上的结理论和数论上的Iwasawa理论之间的类比，重点比较Alexander多项式（拓扑侧）和Iwasawa多项式（数论侧）。我们对这两个对象进行了详细的研究，得出了它们之间的一些很好的一致之处。进一步，为了通过与Alexander多项式的比较发现Iwasawa多项式的一个新性质，我们对Alexander多项式的零点进行了数值计算。

The purpose of our research is to find analogies between knot theory in topology and Iwasawa theory in number theory, focusing on comparison of Alexander polynomials (topology side) and Iwasawa polynomials (number theory side). Studying both objects in detail, we reached some good correspondence between them. Further, aiming at finding a new property of Iwasawa polynomials through comparison to Alexander polynomials, we carried out numerical computation of zeros of Alexander polynomials.