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

Shuji Yamamoto

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)449-476
Number of pages28
JournalMathematische Annalen
Volume346
Issue number2
DOIs
Publication statusPublished - 2009 Nov
Externally publishedYes

Fingerprint

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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

In: Mathematische Annalen, Vol. 346, No. 2, 11.2009, p. 449-476.

Research output: Contribution to journalArticle

Yamamoto, Shuji. / On Shintani's ray class invariant for totally real number fields. In: Mathematische Annalen. 2009 ; Vol. 346, No. 2. pp. 449-476.
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