Experimental Mathematics

Stark's conjectures and Hilbert's twelfth problem

Xavier-François Roblot

Abstract

We give a constructive proof of a theorem of Tate, 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.

Article information

Source
Experiment. Math., Volume 9, Issue 2 (2000), 251-260.

Dates
First available in Project Euclid: 22 February 2003

Permanent link to this document
https://projecteuclid.org/euclid.em/1045952349

Mathematical Reviews number (MathSciNet)
MR1780210

Zentralblatt MATH identifier
0986.11074

Subjects
Primary: 11R42: Zeta functions and $L$-functions of number fields [See also 11M41, 19F27]
Secondary: 11R20: Other abelian and metabelian extensions 11R37: Class field theory

Citation

Roblot, Xavier-François. Stark's conjectures and Hilbert's twelfth problem. Experiment. Math. 9 (2000), no. 2, 251--260. https://projecteuclid.org/euclid.em/1045952349


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