The local zeta function in enumerating quartic fields

DOI10.1016/j.jnt.2019.12.017zbMath1454.11175arXiv1806.01372OpenAlexW2805516687WikidataQ126314999 ScholiaQ126314999MaRDI QIDQ2291700

Robert D. Hough

Publication date: 31 January 2020

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.01372

zbMATH Keywords

exponential sumgroup actionprehomogeneous vector spaceorbit decompositionquartic number fields

Mathematics Subject Classification ID

Asymptotic results on counting functions for algebraic and topological structures (11N45) Exponential sums (11T23) Cubic and quartic extensions (11R16) Prehomogeneous vector spaces (11S90)

Uses Software

• Magma
• Mathematica

Cites Work

• Unnamed Item
• Secondary terms in counting functions for cubic fields
• Prehomogeneous vector spaces and field extensions
• On zeta functions associated with prehomogeneous vector spaces
• The Magma algebra system. I: The user language
• Higher composition laws. III: The parametrization of quartic rings
• Higher composition laws. II: On cubic analogues of Gauss composition
• The shape of cubic fields
• Higher composition laws. IV: The parametrization of quintic rings
• Orbital L-functions for the Space of Binary Cubic Forms
• Orbital exponential sums for prehomogeneous vector spaces
• On Dirichlet series whose coefficients are class numbers of integral binary cubic forms

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