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We give a representation of the classical theory of multiplicative arithmeticfunctions (MF)in the ring of symmetric polynomials. The basis of the ring ofsymmetric polynomials that we use is the isobaric basis, a basis especiallysensitive to the combinatorics of partitions of the integers. The representingelements are recursive sequences of Schur polynomials evaluated at subrings ofthe complex numbers. The multiplicative arithmetic functions are units in theDirichlet ring of arithmetic functions, and their properties can be describedlocally, that is, at each prime number $p$. Our representation is, hence, alocal representation. One such representing sequence is the sequence ofgeneralized Fibonacci polynomials. In general the sequences consist ofSchur-hook polynomials. This representation enables us to clarify andgeneralize classical results, e.g., the Busche-Ramanujan identity, as well asto give a richer structural description of the convolution group ofmultiplicative functions. It is a consequence of the representation that theMF's can be defined in a natural way on the negative powers of the prime $p$.

A Representation of Multiplicative Arithmetic Functions by Symmetric Polynomials