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Discorrelation of the Möbius function with linear phases in short intervals
We introduce a new approach to studying correlations between arithmetic functions and linear phases with respect to highly irrational frequency over short intervals. As an application, we prove that \[ \Big|\sum_{x<n \leq x+H}μ(n) e(nα)\Big| \ll H(\log x)^{-1/3+\varepsilon } \] whenever $x^{0.58+\va
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