Manjul Bhargava (Princeton University): In how many ways can an order in a quartic field be monogenized?

Online Number Theory Seminar

Abstract: We show that an order in a quartic field has fewer than 3000 essentially different generators as a $\mathbb{Z}$-algebra (and fewer than 200 if the discriminant of the order is sufficiently large). This significantly improves the previously best known bound of $2^{72}$.

Analogously, we show that an order in a quartic field is isomorphic to the invariant order of at most 10 classes of integral binary quartic forms (and at most 7 if the discriminant is sufficiently large). This significantly improves the previously best known bound of $2^{80}$.

This time, upon the request of the Speaker, the talk will be given via Zoom.

For access please contact the organizers (ntrg[at]science.unideb.hu).