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Abstract: We give a constructive proof of a theorem given in [Tate 84] which states that (under Stark's Conjecture) the field generated over a totally real field K by the Stark units contains the maximal real Abelian extension of K. As a direct application of this proof, we show how one can compute explicitly real Abelian extensions of K. We give two examples. In a series of important papers [Stark 71, Stark 75, Stark 76, Stark 80] H. M. Stark developed a body of conjectures relating the values of Artin ... (Update)
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...place w of H k which does not divide v. We refer to [22] for this conjecture and a more general statement of Stark s conjectures, and to [17] for a proof of this result. In the next section, we will explain how to compute # # K k (0, #) for # # G, and how to find the element #...
...must be of rank 2. One consequence is that, unlike verifications of the (complex) first order abelian Stark Conjectures (see for example [Ro]) the regulators themselves do not determine S units of K. We therefore need different methods for finding K and j f;T and criteria for...
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BibTeX entry: (Update)
X.-F. Roblot, Stark's Conjectures and Hilbert's Twelfth Problem, preprint; Algorithmes de Factorisation dans les Extensions Relatives et Applications de la Conjecture de Stark a la Construction des Corps de Classes de Rayon, Thesis, Universite Bordeaux I (1997) http://citeseer.ist.psu.edu/roblot99starks.html More
@misc{ roblot97starks,
author = "X. Roblot",
title = "Stark's Conjectures and Hilbert's Twelfth Problem",
text = "X.-F. Roblot, Stark's Conjectures and Hilbert's Twelfth Problem, preprint;
Algorithmes de Factorisation dans les Extensions Relatives et Applications
de la Conjecture de Stark a la Construction des Corps de Classes de Rayon,
Thesis, Universite Bordeaux I (1997)",
year = "1997",
url = "citeseer.ist.psu.edu/roblot99starks.html" }
Citations (may not include all citations):31 Fundamentals of Diophantine Geometry (context) - Lang - 1983
16 Les Conjectures de Stark sur les Fonctions L d'Artin en s (context) - Tate - 1984
8 Explicit Bounds for Primes in Residue Classes (context) - Bach, Sorenson - 1996
7 Conductors and Discriminants (context) - Cohen, Diaz et al. - 1998
6 Bericht uber neuere Untersuchungen und Probleme aus der Theo.. (context) - Hasse - 1965
5 Computing Class Fields via the Artin Map (context) - Fieker - 1997
4 Computations with Relative Extensions of Number Fields with .. (context) - Daberkow, Pohst - 1995
3 Character Theory and Artin L-functions (context) - Martinet - 1977
3 Zeros of Dedekind Zeta Functions in the Critical Strip (context) - Tollis - 1997
2 de la Conjecture de Stark `a la Construction des Corps de Cl.. (context) - Roblot, dans et al. - 1997
2 Algorithmic Techniques for Relative Extensions of Number Fie.. (context) - Cohen, Diaz et al. - 1996
2 Computing the Leading Term of an Abelian L-function (context) - Dummit, Tangedal - 1998
1 Computing the Hilbert Class Field of a Real Quadratic Field - Cohen, Roblot
1 functions with Rational Characters (context) - Stark, at et al. - 1975
1 The Number Theory System PARI (context) - Batut, Belabas et al. - 1999
1 Totally Real Fields and Hilbert's Twelfth Problem (context) - Stark, at - 1976
1 First Derivatives (context) - Stark, at et al. - 1980
1 Computing Stark Units for Totally Real Cubic Fields (context) - Dummit, Sands et al. - 1997
1 functions for quadratic forms (context) - Stark, L-functions et al. - 1971
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Computing The Hilbert Class Field Of Real Quadratic Fields - Cohen, Roblot (1999) (Correct)
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