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  • Author or Editor: A. Balog x
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For an integer n≯1 letP(n) be the largest prime factor of n. We prove that there are infinitely many triplets of consecutive integers with descending largest prime factors, that is P(n - 1) ≯P(n)≯P(n+1) occurs for infinitely many integers n.

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We determine, up to a constant factor, the L 1 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 L 1 norm of the exponential sum defined with the Mbius function.

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