The distribution function of a polynomial in additive functions

  • Noah Lebowitz-LockardEmail author


A real-valued arithmetic function f is said to cluster around a point r if the upper density of inputs n for which f(n) is within \(\delta \) of r does not tend to zero as \(\delta \) goes to zero. If f does not cluster around any real number, then we say that f is nonclustering. We show that the product of nonclustering additive functions is nonclustering and provide a generalization for polynomials of nonclustering additive functions. We then use these results to prove that products of additive functions possessing continuous distribution functions also possess continuous distribution functions.


Distribution functions Additive functions Erdős–Wintner Theorem 

Mathematics Subject Classification




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Authors and Affiliations

  1. 1.University of GeorgiaAthensUSA

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