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SUMMARY:Counting $D_4$-field extensions by multi-invariants
DTSTART:20251208T100000Z
DTEND:20251208T110000Z
DTSTAMP:20260425T212600Z
UID:indico-event-14761@indico.math.cnrs.fr
CONTACT:regis.de-la-breteche@imj-prg.fr
DESCRIPTION:Speakers: Anna Zanoli (IST Austria)\n\nIn joint work with W. H
 ansen\, we count the number of Galois extensions $M/\\mathbb{Q}$ with fixe
 d Galois group $\\text{Gal}(M/\\mathbb{Q})=D_4$ ordered by multi-invariant
 s introduced by Gundlach. Our results verify the asymptotic behavior predi
 cted by Gundlach’s refinement of Malle’s conjecture\, and we further c
 ompare the leading constant to recent predictions of Loughran and Santens.
 In our work\, we combine a parametrization of $D_4$-extensions as quadrati
 c extensions of biquadratic fields with analytic techniques for handling c
 haracter sums. This approach allows us to adapt the methods of Friedlander
 –Iwaniec and of Rome to the setting of $D_4$-octic fields\, ultimately l
 eading to a precise asymptotic and an explicit description of the leading 
 constant.\n\nhttps://indico.math.cnrs.fr/event/14761/
LOCATION:Salle Yvette Cauchois (IHP - Bâtiment Perrin)
URL:https://indico.math.cnrs.fr/event/14761/
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