Dedekind eta and Jacobi theta function identities

Terry Gannon (tgannon@math.ualberta.ca)
University of Alberta
Department of Mathematics
Edmonton, Alberta, T6G 2G1

Abstract

In Gannon-Lam, geometrical lattice equivalences were used to produce identities involving the Jacobi theta functions. Here we strengthen and extend the method, and find identities also involving the Dedekind eta function (and more generally any Dirichlet twists of the theta functions). We find over 100 new quadratic eta function identities and conjecture we've found them all.