Convolution identities for divisor functions

In this talk, we consider exact identities for infinite sums of even divisor 
functions weighted by Laurent polynomials with logarithms for which the sum is 
absolutely convergent. Such identities are motivated by computations in string theory 
related to the scattering of 4-gravitons. We show that in general they give Fourier 
coefficients of holomorphic cusp forms using the method of holomorphic projection 
and discuss an application of spectral techniques to such sums. The talk is based on