CLASS NUMBER PARITY OF A QUADRATIC TWIST OF A CYCLOTOMIC FIELD OF PRIME POWER CONDUCTOR

DOI 機関リポジトリ HANDLE オープンアクセス

この論文をさがす

抄録

Let p be a fixed odd prime number and K_n the p^<n+1>-st cyclotomic field. For a fixed integer d∊Z with √<d>∉K_0, denote by L_n the imaginary quadratic subextension of the biquadratic extension K_n(√<d>)/K_n^+ with L_n≠K_n. Let h^* _n and h^-_n be the relative class numbers of K_n and L_n, respectively. We give an explicit constant nd depending on p and d such that (i) for any integer n≥n_d , the ratio h^-_n/h^-_<n+1> is odd if and only if h^*_n =h^*_<n-1> is odd and (ii) for 1≤n<n_d , h^-_n/h^-_<n-1> is even.

収録刊行物

  • Osaka Journal of Mathematics

    Osaka Journal of Mathematics 50 (2), 563-572, 2013-06

    Osaka University and Osaka City University, Departments of Mathematics

詳細情報 詳細情報について

問題の指摘

ページトップへ