The local zeta function in enumerating quartic fields

Robert D. Hough

doi:10.1016/j.jnt.2019.12.017

The local zeta function in enumerating quartic fields

Robert D. Hough

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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⊗Sym²(Z_p ³) parametrizing quartic fields, thus solving the local ‘quartic case’ in enumerating quartic fields.

Original language	English
Pages (from-to)	1-131
Number of pages	131
Journal	Journal of Number Theory
Volume	210
DOIs	https://doi.org/10.1016/j.jnt.2019.12.017
State	Published - May 2020

Keywords

Exponential sum
Group action
Orbit decomposition
Prehomogeneous vector space
Quartic number fields

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10.1016/j.jnt.2019.12.017

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title = "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⊗Sym2(Zp 3) parametrizing quartic fields, thus solving the local {\textquoteleft}quartic case{\textquoteright} in enumerating quartic fields.",

keywords = "Exponential sum, Group action, Orbit decomposition, Prehomogeneous vector space, Quartic number fields",

author = "Hough, \{Robert D.\}",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

year = "2020",

month = may,

doi = "10.1016/j.jnt.2019.12.017",

language = "English",

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AU - Hough, Robert D.

PY - 2020/5

Y1 - 2020/5

N2 - 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⊗Sym2(Zp 3) parametrizing quartic fields, thus solving the local ‘quartic case’ in enumerating quartic fields.

AB - 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⊗Sym2(Zp 3) parametrizing quartic fields, thus solving the local ‘quartic case’ in enumerating quartic fields.

KW - Exponential sum

KW - Group action

KW - Orbit decomposition

KW - Prehomogeneous vector space

KW - Quartic number fields

UR - https://www.scopus.com/pages/publications/85078350962

U2 - 10.1016/j.jnt.2019.12.017

DO - 10.1016/j.jnt.2019.12.017

M3 - Article

AN - SCOPUS:85078350962

SN - 0022-314X

VL - 210

SP - 1

EP - 131

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

The local zeta function in enumerating quartic fields

Abstract

Keywords

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