CLASS NUMBER PARITY OF A QUADRATIC TWIST OF A CYCLOTOMIC FIELD OF PRIME POWER CONDUCTOR
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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
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- Osaka Journal of Mathematics
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Osaka Journal of Mathematics 50 (2), 563-572, 2013-06
Osaka University and Osaka City University, Departments of Mathematics
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詳細情報 詳細情報について
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- CRID
- 1390572174763979136
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- NII論文ID
- 120005294082
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- NII書誌ID
- AA00765910
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- DOI
- 10.18910/25091
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- HANDLE
- 11094/25091
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- ISSN
- 00306126
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- 本文言語コード
- en
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- データソース種別
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- JaLC
- IRDB
- CiNii Articles