Isobaric polynomials and arithmetic functions
Abstract: In an isomorphic copy of the ring of symmetric polynomials,
isobaric polynomials, we introduce some families indexed by rational weight
vectors. We shall focus on constructing the rational roots of these polynomials
under a product induced by convolution. A direct application is to the
description of the roots of certain multiplicative arithmetic functions (the
"core" group) under the usual convolution product.
This is joint work with Trueman MacHenry.