New recurrence relations and matrix equations for arithmetic functions generated by Lambert series

Abstract

We consider relations between the pairs of sequences $(f, g_f)$ generated by the Lambert series expansions $L_f(q) = \sum_{n \geq 1} f(n) q^n / (1-q^n)$ in $q$ where $g_f(m)$ is defined to be the coefficient of $q^m$ in $L_f(q)$. In particular, we prove n

Locations

• Acta Arithmetica - View
• arXiv (Cornell University) - View - PDF