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 $k\geq 3$.
@article{10_4064_aa8130_5_2016,
author = {Xiaoguang He and Bingrong Huang},
title = {Exponential sums involving the {M\"obius} function},
journal = {Acta Arithmetica},
pages = {201--209},
year = {2016},
volume = {175},
number = {3},
doi = {10.4064/aa8130-5-2016},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa8130-5-2016/}
}
TY - JOUR
AU - Xiaoguang He
AU - Bingrong Huang
TI - Exponential sums involving the Möbius function
JO - Acta Arithmetica
PY - 2016
SP - 201
EP - 209
VL - 175
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4064/aa8130-5-2016/
DO - 10.4064/aa8130-5-2016
LA - en
ID - 10_4064_aa8130_5_2016
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%A Xiaoguang He
%A Bingrong Huang
%T Exponential sums involving the Möbius function
%J Acta Arithmetica
%D 2016
%P 201-209
%V 175
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4064/aa8130-5-2016/
%R 10.4064/aa8130-5-2016
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Xiaoguang He; Bingrong Huang. Exponential sums involving the Möbius function. Acta Arithmetica, Tome 175 (2016) no. 3, pp. 201-209. doi: 10.4064/aa8130-5-2016
