Estimates for smooth Weyl sums on major arcs

Published 28 May 2024 in math.NT | (2405.18608v1)

Abstract: We present estimates for smooth Weyl sums of use on sets of major arcs in applications of the Hardy-Littlewood method. In particular, we derive mean value estimates on major arcs for smooth Weyl sums of degree $k$ delivering essentially optimal bounds for moments of order $u$ whenever $u>2\lfloor k/2\rfloor +4$.

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