On Baker type bounds and generalised transcendence measure (joint work with K. Lepp\"al\"a and Tapani Matala-aho)

Abstract
If $\alpha$ is transcendental, then $P(\alpha)\ne 0$ for all polynomials $P$ with integer coefficients. The transcendence measure tells how far from zero these values of polynomials must be (at least). During my talk, I will first give a sketch of the current knowledge about the transcendence measure of $e$, and I will also briefly explain how these results can be obtained. I will then move to explaining how the transcendence measure can be generalised, and what is known and what is believed about the generalised transcendence measure.