# David Broadhurst: Elliptic integrals in quantum field theory

**Abstract**:

Massless diagrams in quantum field theory often, yet not invariably, evaluate to polylogarithms. With massive propagators, elliptic integrals appear as early as two loops. They are not to be feared, but rather welcomed, since elliptic integrals have amazingly fast numerical evaluations. In the first talk, I shall consider some fairly well-known appearances of elliptic integrals in QFT. In the second, I shall move on to diagrams that evaluate to products of elliptic integrals, which pave the way for more general evaluations, as the L-functions of modular forms at integers inside Dirichlet's critical strip, which likewise have very fast evaluations.