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- W2068281502 abstract "In this elementary note we prove that a polynomial with rational coefficients divides the derivative of some polynomial which splits in <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=double-struck upper Q> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>Q</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathbb Q</mml:annotation> </mml:semantics> </mml:math> </inline-formula> if and only if all of its irrational roots are real and simple. This provides an answer to a question posed by Thomas Craven. Similar ideas also lead to a variation of the proof of Belyi’s theorem that every algebraic curve defined over an algebraic number field admits a map to <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper P Superscript 1> <mml:semantics> <mml:msup> <mml:mi>P</mml:mi> <mml:mn>1</mml:mn> </mml:msup> <mml:annotation encoding=application/x-tex>P^1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> which is only ramified above three points. As it turned out, this variation was noticed previously by G. Belyi himself and Leonardo Zapponi." @default.
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- W2068281502 date "2003-07-02" @default.
- W2068281502 modified "2023-09-25" @default.
- W2068281502 title "On a question of Craven and a theorem of Belyi" @default.
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- W2068281502 doi "https://doi.org/10.1090/s0002-9939-03-07151-x" @default.
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