Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On a question of Craven and a theorem of Belyi
HTML articles powered by AMS MathViewer

by Alexander Borisov PDF
Proc. Amer. Math. Soc. 131 (2003), 3677-3679 Request permission

Abstract:

In this elementary note we prove that a polynomial with rational coefficients divides the derivative of some polynomial which splits in $\mathbb Q$ 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 $P^1$ which is only ramified above three points. As it turned out, this variation was noticed previously by G. Belyi himself and Leonardo Zapponi.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11R80, 11G99
  • Retrieve articles in all journals with MSC (2000): 11R80, 11G99
Additional Information
  • Alexander Borisov
  • Affiliation: Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802
  • Email: borisov@math.psu.edu
  • Received by editor(s): July 19, 2002
  • Published electronically: July 2, 2003
  • Communicated by: David E. Rohrlich
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 3677-3679
  • MSC (2000): Primary 11R80; Secondary 11G99
  • DOI: https://doi.org/10.1090/S0002-9939-03-07151-X
  • MathSciNet review: 1998173