TY - JOUR
T1 - On Shintani's ray class invariant for totally real number fields
AU - Yamamoto, Shuji
N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.
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.
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U2 - 10.1007/s00208-009-0405-x
DO - 10.1007/s00208-009-0405-x
M3 - Article
AN - SCOPUS:76149138014
SN - 0025-5831
VL - 346
SP - 449
EP - 476
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 2
ER -