We express products of Lambert series as power series. We use these Lambert series-to-power series identities to obtain new Liouville identities with two functions. Many of the known Liouville identities follow from our new identities. We explore the relationships between Lambert series, new Liouville identities, and convolution sums. We then obtain recursive formulae for various convolution sums.

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Keywords convolution sums, divisor functions, Lambert series, Liouville identities, power series, twisted convolution sums
Persistent URL dx.doi.org/10.1142/S1793042116500822
Journal International Journal of Number Theory
Alaca, S, & Doyle, G. (Greg). (2016). Liouville identities with two functions. International Journal of Number Theory, 12(5), 1345–1363. doi:10.1142/S1793042116500822