Liouville identities with two functions
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.
|Keywords||convolution sums, divisor functions, Lambert series, Liouville identities, power series, twisted convolution sums|
|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