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

Shuji Yamamoto

研究成果: Article

1 引用 (Scopus)

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) = 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.

元の言語English
ページ(範囲)449-476
ページ数28
ジャーナルMathematische Annalen
346
発行部数2
DOI
出版物ステータスPublished - 2009 11
外部発表Yes

Fingerprint

Number field
Half line
Sum formula
Invariant
L-function
Factorization
Cone
Signature
Decompose
Derivative
Unit
Class

ASJC Scopus subject areas

  • Mathematics(all)

これを引用

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

:: Mathematische Annalen, 巻 346, 番号 2, 11.2009, p. 449-476.

研究成果: Article

Yamamoto, Shuji. / On Shintani's ray class invariant for totally real number fields. :: Mathematische Annalen. 2009 ; 巻 346, 番号 2. pp. 449-476.
@article{112ad45d504b47e6bf5b3dc316a6f219,
title = "On Shintani's ray class invariant for totally real number fields",
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) = 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.",
author = "Shuji Yamamoto",
year = "2009",
month = "11",
doi = "10.1007/s00208-009-0405-x",
language = "English",
volume = "346",
pages = "449--476",
journal = "Mathematische Annalen",
issn = "0025-5831",
publisher = "Springer New York",
number = "2",

}

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 -