Hall 123

Roots of Irreducible Polynomials and their Clusters

P Vanchinathan

VIT Chennai

For a root alpha of an irreducible polynomial f(x) in Q[x], how many roots of f(x) are found in the field Q(alpha)?

Strangely this question seems to have not been addressed in the 19th or 20th century.

After discussing the wonderful answer of Alexander Perlis in 2004, we describe our work which gives a new machinery for finding polynomials with 'custom' number of roots in Q(alpha).