*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.