Vers un théorème de Cobham pour les entiers de Gauss

Abstract

Let $p$ and $q$ be two distinct positive integers and let $\alpha=-p+i$ and $\beta=-q+i$. Assuming that {\it the four exponentials conjecture\/} is true, it is shown that if a set $S$ of Gaussian integers is $(\alpha,\beta)$-recognizable, then it is syndetic.