Date: Tuesday 4 October 2022


The modern practitioner of zeta functions tends to work with Haar integrals over locally compact groups. This is a far cry from our familiar representation of the Riemann zeta function as a Dirichlet series or as an Euler product. Nonetheless, Tate’s Thesis (1950) makes a convincing case for adopting this more abstract perspective. It turns out that the study of many other classical generating functions can be enriched through abstract harmonic analysis e.g. Cauchy’s q-binomial series, Eisenstein-Hermite’s integral lattice generating function, Euler’s partition generating function, and Erdos-Szekeres’ abelian group generating function. We see this by relating our classical generating functions to zeta functions of arithmetic modules, which are originally defined as Dirichlet series.


Sean Lynch 


UNSW, Sydney


Tuesday 4 October 2022, 12 noon