Building bases for analytical fits of four-loop QED master integrals

Abstract

In this paper I will briefly describe how to find some elements of the basis necessary for the PSLQ fits of master integrals that appear in the calculation of four-loop contributions to the electron $g$-$2$ and the renormalization constants in QED. In particular we consider master integrals containing polylogarithms of the sixth root of the unity and elliptical integrals. A new high-precision numerical determination of $Z_2$ at four loops will be also shown.