A Measure of Simultaneous Approximation for Quasi-Modular Functions

We improve on a recent result of Saradha giving a transcendence measure for the quotient ŋ ω of a period of an elliptic curve defined over ℚ by its associated quasi-period. In an (“almost” successful) attempt to include in a single measure both this result and that obtained by Reyssat in 1980, we blend into the “modular method” ideas related to modular but also hypergeometric functions, as appearing e.g. in André's work, as well as some Galois considerations.