Affiliation: University of Rochester
Email: hahn@math.rochester.edu
Title Of Talk: Convolution sums of functions on divisors
Abstract: In this talk, we derive convolution sums of functions for the divisor sums $\tilde{\sigma}}_s(n):=\sum_{d|n}(-1)^{d-1}d^s$ and $\hat{\sigma}}_s(n):=\sum_{d|n}(-1)^{n/d-1}d^s$ for certain $s$, which were first defined by Glaisher. We then discuss some formulae for determining $r_s(n)$ and $\delta_s(n)$, $s=4,8$, in terms of thses divisor functions, where as usual, $r_s(n)$ and $\detla_s(n)$ denote the number of representations of $n$ as a sum of $s$ squares and $s$ triangular numbers, respectively.
Last update made Thu Nov 11 14:46:30 EST 2004.
Please report problems to:
frank@math.ufl.edu