Twisted zeta-functions and abelian Stark Conjectures

TY - JOUR

T1 - Twisted zeta-functions and abelian Stark Conjectures

AU - Solomon, D

PY - 2002

Y1 - 2002

N2 - We present a new version "at s = 1" of Rubin's refined, higher order Stark conjecture at s = 0 for an abelian extension of number fields (K. Rubin, 1996, Ann. Inst. Fourier 46, No. 1, 33-62). The key idea is to introduce a formalism of "twisted zeta-functions" to replace the L-functions underlying Rubin's conjecture. This achieves certain simplifications, notably eliminating Gauss sums in a natural way from our version at s = 1. It also facilitates some further developments, including an important motivation of the present paper: the formulation of an analogous p-adic conjecture to be presented in a sequel. (C) 2002 Elsevier Science (USA).

AB - We present a new version "at s = 1" of Rubin's refined, higher order Stark conjecture at s = 0 for an abelian extension of number fields (K. Rubin, 1996, Ann. Inst. Fourier 46, No. 1, 33-62). The key idea is to introduce a formalism of "twisted zeta-functions" to replace the L-functions underlying Rubin's conjecture. This achieves certain simplifications, notably eliminating Gauss sums in a natural way from our version at s = 1. It also facilitates some further developments, including an important motivation of the present paper: the formulation of an analogous p-adic conjecture to be presented in a sequel. (C) 2002 Elsevier Science (USA).

UR - http://www.scopus.com/inward/record.url?scp=0036268233&partnerID=8YFLogxK

U2 - 10.1006/jnth.2001.2724

DO - 10.1006/jnth.2001.2724

M3 - Article

VL - 94

SP - 10

EP - 48

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 1

ER -