Distributional Properties of the Largest Prime Factor

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Distributional Properties of the Largest Prime Factor

Please use this identifier to cite or link to this item: http://hdl.handle.net/10355/10840

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Title: Distributional Properties of the Largest Prime Factor
Author: Banks, William David, 1964-; Harman, G. (Glyn), 1956-; Shparlinski, Igor E.
Keywords: distributive properties
integers
Date: 2005
Publisher: University of Michigan
Citation: Michigan Math. J. 53 (2005), 665-681.
Abstract: Let P(n) denote the largest prime factor of an integer n ≥ 2, and put P(1) = 1. In this paper, we study the distribution of the sequence {P(n) : n ≥ 1} over the set of congruence classes modulo an integer q ≥ 2, and we study the same question for the sequence {P(p − 1) : p is prime}. We also give bounds for rational exponential sums involving P(n). Finally, for an irrational number _, we show that the sequence {_P(n) : n ≥ 1} is uniformly distributed modulo 1.
URI: http://hdl.handle.net/10355/10840
ISSN: 0026-2285

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  • Mathematics publications (MU) [119]
    The items in this collection are the scholarly output of the faculty, staff, and students of the Department of Mathematics.

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