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The Hermite–Joubert Problem and a Conjecture of Brassil and Reichstein

  • Khoa Dang Nguyen (a1)

We show that Hermite’s theorem fails for every integer $n$ of the form $3^{k_{1}}+3^{k_{2}}+3^{k_{3}}$ with integers $k_{1}>k_{2}>k_{3}\geqslant 0$ . This confirms a conjecture of Brassil and Reichstein. We also obtain new results for the relative Hermite–Joubert problem over a finitely generated field of characteristic 0.

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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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