We give asymptotic formulas for the number of biquadratic extensions of $ \mathbb{Q}$ that admit a quadratic extension which is a Galois extension of $ \mathbb{Q}$ with a prescribed Galois group, for example, with a Galois group isomorphic to the quaternionic group. Our approach is based on a combination of the theory of quadratic equations with some analytic tools such as the Siegel-Walfisz theorem and the double oscillations theorem.
Pappalardi, F., Fouvry, E., Luca, F., Shparlinski, I. (2011). Counting dihedral and quaternionic extensions. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 363(6), 3233-3253 [10.1090/S0002-9947-2011-05233-5].
Counting dihedral and quaternionic extensions
PAPPALARDI, FRANCESCO;
2011-01-01
Abstract
We give asymptotic formulas for the number of biquadratic extensions of $ \mathbb{Q}$ that admit a quadratic extension which is a Galois extension of $ \mathbb{Q}$ with a prescribed Galois group, for example, with a Galois group isomorphic to the quaternionic group. Our approach is based on a combination of the theory of quadratic equations with some analytic tools such as the Siegel-Walfisz theorem and the double oscillations theorem.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
