L-series of squares of squares

The book by Hardy and Wright records elegant forms for the Dirichlet generating functions of the divisor functions $\sigma_k(n)=\sum_{d\,|\,n}d^k$ and $\sigma_k^2(n)$. This talk extends such evaluations by providing a general indentity for Dirichlet convolutions of completely multiplicative sequences. Applications are given to the number of representations of integers as sums of squares. (Based on joint work with Stephen Choi, CECM Preprint 01:167 at {\sf www.cecm.sfu.ca/preprints}.)