Title: The shape of cubic and quartic fields
Speaker: Bob Hough (Stony Brook University)
Abstract: I introduce a new zeta function on the space of binary cubic forms, and the space of pairs of ternary quadratic forms, which is twisted by a cusp form. I show that these zeta functions are entire. Combined with a method of Taniguchi-Thorne, I obtain equidistribution of the shape of cubic fields, and of the joint shape of a quartic field and it's cubic resolvent ring, when fields are ordered by discriminant. Here the shape of a number field is understood to be the shape of the ring of integers viewed as a lattice in the canonical embedding, and projected in the direction orthogonal to 1.
Seminar URL: https://research.math.osu.edu/numbertheory/number.php
