### Abstract

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.

Original language | English |
---|---|

Pages (from-to) | 449-476 |

Number of pages | 28 |

Journal | Mathematische Annalen |

Volume | 346 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2009 Nov |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*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.

Research output: Contribution to journal › Article

*Mathematische Annalen*, vol. 346, no. 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 -