The local zeta function in enumerating quartic fields

Abstract

An exact formula is obtained for the Fourier transform of the local condition of maximality modulo primes $p>3$ in the prehomogeneous vector space $2\otimes {\mathrm{Sym}}^2({\mathbb{Z}}_p^3)$ parametrizing quartic fields, thus solving the local `quartic case' in enumerating quartic fields.

Minor corrections

References in corpus (4)

• Secondary terms in counting functions for cubic fields
• Orbital L-functions for the space of binary cubic forms
• Orbital exponential sums for prehomogeneous vector spaces
• The shape of quartic fields

Cited by in corpus (1)

• Eisenstein series twisted Shintani zeta function