## Isobaric polynomials and arithmetic functions

**G. Tudose **

(York U.)

Abstract: In an isomorphic copy of the ring of symmetric polynomials,
that is,

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.