Note on heath-brown's estimate for heilbronn's exponential sum

摘要

We show that S_h(a) = sum_(n = 1)~p e((an~(hp))/(p~2)) (h, p - 1)p~(11/12), which generalizes Heath-Brown's estimate for Heilbronn's exponential sum S_1(a). We also give a simple proof of a crucial lemma in Heath-Brown's work.