Abstract
We discuss arithmetic questions related to the 'poor man's adèle ring' A whose elements are encoded by sequences (tp)p indexed by prime numbers, with each tp viewed as a residue in Z/pZ . Our main theorem is about the A -transcendence of the element (Fp(q))p , where Fn(q) (Schur's q-Fibonacci numbers) are the (1, 1)-entries of 2 × 2 -matrices [Formula: see text] and q > 1 is an integer. This result was previously known for q > 1 square free under the GRH.