The shape of quartic fields

Abstract

We use the method of Shintani, as developed by Taniguchi and Thorne, to prove the joint cuspidal equidistribution of the shape of quartic fields paired with the shape of its cubic resolvent, when the fields are ordered by discriminant. Our estimate saves a small power in the corresponding Weyl sums.

Added acknowledgement of financial support from NSF Grant DMS-1712682 "Probabilistic methods in discrete structures and applications."

References in corpus (1)

• Orbital L-functions for the space of binary cubic forms

Cited by in corpus (1)

• The local zeta function in enumerating quartic fields