### 抄録

We introduce a ray class invariant X(C) for a totally real field, following Shintani's work in the real quadratic case. We prove a factorization formula X(C) = X_{n}(C) · · · X_{n}(C) where each X_{i}(C) corresponds to a real place. Although this factorization depends a priori on some choices (especially on a cone decomposition), we can show that it is actually independent of these choices. Finally, we describe the behavior of X_{i}(C) when the signature of C at a real place is changed. This last result is also interpreted in terms of the derivatives L′(0, χ) of the L-functions and certain Stark units.

元の言語 | English |
---|---|

ページ（範囲） | 449-476 |

ページ数 | 28 |

ジャーナル | Mathematische Annalen |

巻 | 346 |

発行部数 | 2 |

DOI | |

出版物ステータス | Published - 2009 11 |

外部発表 | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)

### これを引用

*Mathematische Annalen*,

*346*(2), 449-476. https://doi.org/10.1007/s00208-009-0405-x

**On Shintani's ray class invariant for totally real number fields.** / Yamamoto, Shuji.

研究成果: Article

*Mathematische Annalen*, 巻. 346, 番号 2, pp. 449-476. https://doi.org/10.1007/s00208-009-0405-x

}

TY - JOUR

T1 - On Shintani's ray class invariant for totally real number fields

AU - Yamamoto, Shuji

PY - 2009/11

Y1 - 2009/11

N2 - We introduce a ray class invariant X(C) for a totally real field, following Shintani's work in the real quadratic case. We prove a factorization formula X(C) = Xn(C) · · · Xn(C) where each Xi(C) corresponds to a real place. Although this factorization depends a priori on some choices (especially on a cone decomposition), we can show that it is actually independent of these choices. Finally, we describe the behavior of Xi(C) when the signature of C at a real place is changed. This last result is also interpreted in terms of the derivatives L′(0, χ) of the L-functions and certain Stark units.

AB - We introduce a ray class invariant X(C) for a totally real field, following Shintani's work in the real quadratic case. We prove a factorization formula X(C) = Xn(C) · · · Xn(C) where each Xi(C) corresponds to a real place. Although this factorization depends a priori on some choices (especially on a cone decomposition), we can show that it is actually independent of these choices. Finally, we describe the behavior of Xi(C) when the signature of C at a real place is changed. This last result is also interpreted in terms of the derivatives L′(0, χ) of the L-functions and certain Stark units.

UR - http://www.scopus.com/inward/record.url?scp=76149138014&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=76149138014&partnerID=8YFLogxK

U2 - 10.1007/s00208-009-0405-x

DO - 10.1007/s00208-009-0405-x

M3 - Article

AN - SCOPUS:76149138014

VL - 346

SP - 449

EP - 476

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

IS - 2

ER -