理学部

中野 伸

ナカノ シン  (Shin Nakano)

基本情報

所属
学習院大学 理学部 数学科 教授
学位
理学博士(学習院大学)
Doctor of Science(Gakushuin University)

J-GLOBAL ID
200901017184942630
researchmap会員ID
1000210681

外部リンク

経歴

 11

委員歴

 1

論文

 15
  • Yoshichika IIZUKA, Yutaka KONOMI, Shin NAKANO
    Tokyo Journal of Mathematics 44(1) 33-47 2021年6月  査読有り
  • Yoshichika Iizuka, Yutaka Konomi, Shin Nakano
    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN 68(2) 899-915 2016年4月  査読有り
    Let l be the prime 3, 5 or 7 and let m be a nonzero integer. We give a method for constructing an infinite family of pairs of quadratic fields Q(root D) and Q(root mD) with both class numbers divisible by l. Such quadratic fields are parametrized by rational points on a specified elliptic curve.
  • Shin Nakano
    JOURNAL OF NUMBER THEORY 129(12) 2943-2951 2009年12月  査読有り
    We give a family of quintic cyclic fields with even class number parametrized by rational points on an elliptic curve associated with Emma Lehmer's quintic polynomial Further. we use the arithmetic of elliptic curves and the Chebotarev density theorem to show that there are infinitely many such fields. (C) 2009 Elsevier Inc All rights reserved.
  • Nakano Shin, Sase Masahiko
    Tokyo Journal of Mathematics 25(1) 197-203 2002年  査読有り
    Let p be an odd prime and r a divisor of p - 1. We present a characterization of metacyclic extensions of degree pr containing a given cyclic extension of degree r over a field of characteristic other than p. Furthermore, we give a method of constructing polynomials with Galois groups which are Frobenius groups of degree p. © 2002 by the University of Notre Dame. All rights reserved.
  • T Komatsu, S Nakano
    NAGOYA MATHEMATICAL JOURNAL 164 133-146 2001年12月  査読有り
    Let K/k be a Galois extension of a number field of degree n and p a prime number which does not divide n. The study of the p-rank of the ideal class group of K by using those of intermediate fields of K/k has been made by Iwasawa, Masley et al., attaining the results obtained under respective constraining assumptions. In the present paper we shall show that we can remove these assumptions, and give more general results under a unified viewpoint. Finally, we shall add a remark on the class numbers of cyclic extensions of prime degree of Q.

MISC

 18

書籍等出版物

 1

講演・口頭発表等

 4

共同研究・競争的資金等の研究課題

 13