English

36 Pages

Gain access to the library to view online

__
Learn more
__

Description

Niveau: Supérieur, Doctorat, Bac+8

Verifying a p-Adic Abelian Stark Conjecture at s = 1 X.-F. Roblot IGD, Universite Lyon I D. Solomon ? King's College London November 3, 2003 Abstract In a previous paper [13], the second author developed a new approach to the abelian p-adic Stark conjecture at s = 1 and stated related conjectures. The aim of the present paper is to develop and apply techniques to numerically investigate one of these – the ‘Weak Refined Combined Conjecture' – in fifteen cases. 1 Introduction In the 1970's and 80's Harold Stark [14] made a series of conjectures concerning the values at s = 1 and s = 0 of complex Artin L-series attached to a Galois extension of number fields K/k. Subsequently, much theoretical and computational work has been done, extend- ing and testing these conjectures, with particular attention paid recently to certain refined conjectures in the case where K/k is abelian ([7], [5]). In [13], a new approach to the abelian case of the p-adic conjecture at s = 1 was developed and several related conjectures were stated. The main aim of the present paper is to develop and apply techniques to numerically investigate one of these – the ‘Weak Refined Combined Conjecture' (Conjecture 3.6 of [13], here Conjecture 2.2) – in a number of cases.

Verifying a p-Adic Abelian Stark Conjecture at s = 1 X.-F. Roblot IGD, Universite Lyon I D. Solomon ? King's College London November 3, 2003 Abstract In a previous paper [13], the second author developed a new approach to the abelian p-adic Stark conjecture at s = 1 and stated related conjectures. The aim of the present paper is to develop and apply techniques to numerically investigate one of these – the ‘Weak Refined Combined Conjecture' – in fifteen cases. 1 Introduction In the 1970's and 80's Harold Stark [14] made a series of conjectures concerning the values at s = 1 and s = 0 of complex Artin L-series attached to a Galois extension of number fields K/k. Subsequently, much theoretical and computational work has been done, extend- ing and testing these conjectures, with particular attention paid recently to certain refined conjectures in the case where K/k is abelian ([7], [5]). In [13], a new approach to the abelian case of the p-adic conjecture at s = 1 was developed and several related conjectures were stated. The main aim of the present paper is to develop and apply techniques to numerically investigate one of these – the ‘Weak Refined Combined Conjecture' (Conjecture 3.6 of [13], here Conjecture 2.2) – in a number of cases.

- also write
- valued function
- class field
- over
- let wm
- group-ring-valued ‘regulator maps'
- can unambiguously define

Subjects

Informations

Published by | mijec |

Reads | 16 |

Language | English |

Report a problem