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Résumé En s’inspirant des méthodes employées par Masser pour la fonction zêta de Riemann dans son article (Masser in J Number Theory 131:2037–2046, 2011), on démontre un nouveau lemme de zéros pour les polynômes en z et 1/Γ(z) et on en déduit l’existence pour tout $${n\geq2}$$ n ≥ 2 d’un réel positif C(n) tel que le nombre de rationnels de dénominateur au plus $${D \geq 3}$$ D ≥...