Numerical Verification of the Brumer-Stark Conjecture

Xavier-François Roblot (1) , Brett Tangedal (2)

1 CICMA - Centre interuniversitaire en calcul mathématique algébrique [Montréal]
2 Department of Mathematics

We study the Brumer-Stark conjecture computationally in the simplest situation in which it is unproven: an extension K/k with k quadratic, Gal(K/k) isomorphic to ℤ/4ℤ, the class group of K non trivial, K/ℚ non Galois. We verify the conjecture in 379 such cases and study the problem of whether the power of 2 dividing the Brumer element can be replaced by a lower 2-power so that the result remains true.

Domaines: Théorie des nombres [math.NT]

Xavier-François Roblot, Brett Tangedal. Numerical Verification of the Brumer-Stark Conjecture. Algorithmic Number Theory (ANTS-IV), 2000, Leiden, Netherlands. pp.491-504. ⟨hal-00863022⟩