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Binary quartic forms
with bounded invariants and small Galois groups
Cindy (Sin Yi) Tsang and Stanley Yao Xiao |
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Vol. 302 (2019), No. 1, 249–291
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Abstract |
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We consider integral and irreducible binary quartic forms whose Galois group is isomorphic to a subgroup of the dihedral group of order eight. We first show that the set of all such forms is a union of families indexed by integral binary quadratic forms of nonzero discriminant. Then, we shall enumerate the -equivalence classes of all such forms associated to a fixed . |
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Keywords
binary quartic forms, coregular spaces, arithmetic
statistics
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Mathematical Subject Classification 2010
Primary: 11E76, 11R45
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Milestones
Received: 27 February 2018
Revised: 21 October 2018
Accepted: 26 January 2019
Published: 5 November 2019
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Authors |
| Cindy (Sin Yi) Tsang | |
| Yau Mathematical Sciences
Center Tsinghua University Beijing China |
School of Mathematics (Zhuhai) Sun Yat-Sen University Tangjiawan, Zhuhai Guangdong China |
| Stanley Yao Xiao | |
| Mathematical Institute University of Oxford United Kingdom |
Department of Mathematics University of Toronto Canada |
