Exponential sums involving the Möbius function
Volume 175 / 2016
Acta Arithmetica 175 (2016), 201-209
MSC: 11L03, 11L20.
DOI: 10.4064/aa8130-5-2016
Published online: 15 September 2016
Abstract
Let $\mu (n)$ be the Möbius function, and $e(x)=e^{2\pi ix}$ with $x$ real. We estimate exponential sums involving the Möbius function $$ S_k(x,\alpha )= \sum _{n\leq x}\mu (n)e(n^k\alpha ) $$ under the weak Generalized Riemann Hypothesis when $k\geq 3$.
