On Hau's lemma

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12 Citations (Scopus)


Let f [formula omitted] [formula omitted][X] and let q be a prime power pl(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.

Original languageEnglish
Pages (from-to)451-458
Number of pages8
JournalBulletin of the Australian Mathematical Society
Issue number3
Publication statusPublished - Dec 1994


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