# The local zeta function in enumerating quartic fields

@inproceedings{Hough2018TheLZ,
title={The local zeta function in enumerating quartic fields},
author={Robert D. Hough},
year={2018}
}
• Robert D. Hough
• Published 2018
• Mathematics
• 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.

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#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 13 REFERENCES

## Higher composition laws III: The parametrization of quartic rings

VIEW 10 EXCERPTS
HIGHLY INFLUENTIAL

## Orbital exponential sums for prehomogeneous vector spaces

• Mathematics
• 2016
VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

## The shape of quartic fields

VIEW 2 EXCERPTS

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

• Mathematics
• 2011
VIEW 1 EXCERPT

## Secondary terms in counting functions for cubic fields

• Mathematics
• 2011
VIEW 1 EXCERPT

## Higher composition laws IV: The parametrization of quintic rings

VIEW 1 EXCERPT

## Higher composition laws II: On cubic analogues of Gauss composition

VIEW 1 EXCERPT

## The Magma Algebra System I: The User Language

• Mathematics, Computer Science
• J. Symb. Comput.
• 1997
VIEW 2 EXCERPTS

## Shintani zeta functions

VIEW 1 EXCERPT