On the number of monogenizations of a quartic order (with an appendix by Shabnam Akhtari)

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Abstract

We show that an order in a quartic field has fewer than 3000 essentially different generators as a Z-algebra (and fewer than 200 if the discriminant of the order is sufficiently large). This significantly improves the previously best known bound of 272. Analogously, we show that an order in a quartic field is isomorphic to the invariant order of at most 10 classes of integral binary quartic forms (and at most 7 if the discriminant is sufficiently large).

Original languageEnglish (US)
Pages (from-to)513-531
Number of pages19
JournalPublicationes Mathematicae
Volume100
Issue number3-4
DOIs
StatePublished - 2022

All Science Journal Classification (ASJC) codes

  • General Mathematics

Keywords

  • Thue equation
  • binary form
  • invariant order
  • monogenic
  • number field
  • quartic field
  • quartic order

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