Heilbronn’s exponential sum- Heath Brown

Using Stepanov’s method with auxilliary polynomials inspired from Transcedence theory Heath-Brown get cancellation in Heilbronn’s exponential sum

\displaystyle S(a, p)=\sum_{n=1}^{p} e\left(\frac{a n^{p}}{p^{2}}\right) \ll p^{7 / 8}

uniformly for p \not | a.

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