Alexander polynomials of knots and number theory

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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.