Danylo Radchenko: Convolution identities for sums of even powers of divisors

Abstract:

As a part of asymptotic calculation of correlation functions in \(N=4\) supersymmetric Yang-Mills theory, Chester, Green, Pufu, Wang, and Wen have conjectured an unusual-looking weighted convolution identity involving the sum of squares of divisors function \(\sigma_2\). I will talk about a proof of this conjecture as well as a more general class of similar identities, which turn out to involve Fourier coefficients of cusp forms for \(\mathrm{SL}_2(\mathbb{Z})\). The talk is based on a recent joint work with Ksenia Fedosova and Kim Klinger-Logan.