TY - JOUR
T1 - Counting dihedral and quaternionic extensions
AU - Fouvry, Étienne
AU - Luca, Florian
AU - Pappalardi, Francesco
AU - Shparlinski, Igor E.
PY - 2011/6
Y1 - 2011/6
N2 - We give asymptotic formulas for the number of biquadratic extensions of ℚ that admit a quadratic extension which is a Galois extension of 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.
AB - We give asymptotic formulas for the number of biquadratic extensions of ℚ that admit a quadratic extension which is a Galois extension of 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.
UR - http://www.scopus.com/inward/record.url?scp=79952175158&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-2011-05233-5
DO - 10.1090/S0002-9947-2011-05233-5
M3 - Article
AN - SCOPUS:79952175158
SN - 0002-9947
VL - 363
SP - 3233
EP - 3253
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 6
ER -