Abstract
We prove a nontrivial upper bound for the quantity (with $\mathbf{e}(z)=e^{2\pi iz}$),
\[\biggl\vert \sum_{X\le n\le 2X}\lambda (n)\mathbf{e}(\alpha{\sqrt{n}} )\biggr\vert ,\]
where $\alpha$ is any nonzero real number. This upper bound is an improvement of the earlier known results.
Citation
Ayyadurai Sankaranarayanan. "On the estimation of nonlinear twists of the Liouville function." Illinois J. Math. 56 (2) 551 - 569, Summer 2012. https://doi.org/10.1215/ijm/1385129964
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