Simultaneous approximation to values of the exponential function over the adeles

Abstract

We show that Hermite's approximations to values of the exponential function at given algebraic numbers are nearly optimal when considered from an adelic perspective. We achieve this by taking into account the ratio of these values whenever they make sense in the various completions (Archimedean or $p$-adic) of a number field containing these algebraic numbers.

arXiv comment33 pages, 1 figure; a French version was posted earlier as arXiv:1905.00343