On Cauchy¿Liouville¿Mirimanoff Polynomials

• Autores: Pavlos Tzermias
• Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 50, Nº 2, 2007, pág. 313
• Idioma: inglés
• DOI: 10.4153/cmb-2007-030-7
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• Resumen

  • Let p be a prime greater than or equal to 17 and congruent to 2 modulo 3. We use results of Beukers and Helou on Cauchy¿Liouville¿Mirimanoff polynomials to show that the intersection of the Fermat curve of degree p with the line X + Y = Z in the projective plane contains no algebraic points of degree d with 3 leq d leq 11. We prove a result on the roots of these polynomials and show that, experimentally, they seem to satisfy the conditions of a mild extension of an irreducibility theorem of Pólya and Szegö. These conditions are conjecturally also necessary for irreducibility.