Counting D4-field extensions by multi-invariants
Abstract
We count the number of Galois extensions M/Q with fixed Galois group Gal(M/Q)=D4 ordered by multi-invariants introduced by Gundlach. We verify the asymptotic behavior predicted by Gundlach's version of Malle's conjecture. We compare the leading constant to recent predictions by Loughran and Santens.
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