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We show that if an essentially arbitrary sequence supported on an interval containing $x$ integers, is convolved with a tiny Siegel-Walfisz-type sequence supported on an interval containing $\exp((\log x)^{\varepsilon})$ integers then the resulting multiplicative convolution has (in a weak sense) level of distribution $x^{1/2 + 1/66 - \varepsilon}$ as $x$ goes to infinity.
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P. Shiu · 1980
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B. Green · 2018
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É. Fouvry and M. Radziwiłł
Cited in the paper.
Bombieri-Vinogradov for multiplicative functions, and beyond the x 1 / 2 x^{1/2} -barrier
A. Granville and X. Shao
Cited in the paper.