✦ LIBER ✦
Twisted Zeta-Functions and Abelian Stark Conjectures
✍ Scribed by David Solomon
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 298 KB
- Volume
- 94
- Category
- Article
- ISSN
- 0022-314X
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✦ Synopsis
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.