Nonlinear exponential twists of the Liouville function |
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Authors: | Qingfeng Sun |
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Institution: | 1. School of Mathematics and Statistics, Shandong University at Weihai, Weihai, Shandong, 264209, China
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Abstract: | Let λ(n) be the Liouville function. We find a nontrivial upper bound for the sum
$
\sum\limits_{X \leqslant n \leqslant 2X} {\lambda (n)e^{2\pi i\alpha \sqrt n } } ,0 \ne \alpha \in \mathbb{R}
$
\sum\limits_{X \leqslant n \leqslant 2X} {\lambda (n)e^{2\pi i\alpha \sqrt n } } ,0 \ne \alpha \in \mathbb{R}
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