location:  Publications → journals
Search results

Search: MSC category 12D05 ( Polynomials: factorization )

 Expand all        Collapse all Results 1 - 1 of 1

1. CMB 2007 (vol 50 pp. 313)

Tzermias, Pavlos
 On Cauchy--Liouville--Mirimanoff Polynomials 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 P\'{o}lya and Szeg\"{o}. These conditions are \emph{conjecturally} also necessary for irreducibility. Categories:11G30, 11R09, 12D05, 12E10
 top of page | contact us | privacy | site map |