Counting dihedral and quaternionic extensions

Étienne Fouvry*, Florian Luca, Francesco Pappalardi, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)3233-3253
Number of pages21
JournalTransactions of the American Mathematical Society
Volume363
Issue number6
DOIs
Publication statusPublished - Jun 2011

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