On Hau's lemma

Let f [formula omitted] [formula omitted][X] and let q be a prime power p^l(l ≥ 2). Hua stated and proved that [formula omitted] for some unspecified constant C > 0 depending on the derivative f^′ of f; M denoting the maximum multiplicity of the roots of the congruence p^−t f^′(x) ≡ 0 (mod p), where t is an integer chosen so that the polynomial p^−t f^′(x) is primitive. An explicit value for C was given by Chalk for p ≥ 3. Subsequently, Ping Ding (in two successive articles) obtained better estimates for p ≥ 2. This article provides a better result, based upon a more precise form of Hua's main lemma, previously overlooked.