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In this paper, we investigate the explicit formulae for the uniformizers of the false Tate curve extension of ℚ p . More precisely, we establish the formulae for the fields p m , 1 = ℚ p (ζ p m , p 1 / p) with m ≥ 1 and for general n ≥ 2 , we prove the existence of the recurrence polynomials ℛ p m , n for general field extensions p m , n of ℚ p , which shows the possibility to construct the uniformizers systematically. [ABSTRACT FROM AUTHOR]