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  • 1 ALFRÉD RÉNYI MATHEMATICAL INSTITUTE BUDAPEST 1364 P.O.BOX 127 BUDAPEST 1364 P.O.BOX 127
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Abstract  

We determine, up to a constant factor, the L1 mean of the exponential sum formed with the r-free integers. This improves earlier results of Brdern, Granville, Perelli, Vaughan and Wooley. As an application, we improve the known bound for the L1 norm of the exponential sum defined with the Mbius function.

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