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Uniform distribution of the fractional part of the average prime divisor
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William D. Banks
Published/Copyright:
November 18, 2005
Abstract
We estimate exponential sums with the function ρ (n ) defined as the average of the prime divisors of an integer n ≥ 2 (we also put ρ (1) = 0). Our bound implies that the fractional parts of the numbers { ρ (n ) : n ≥ 1 } are uniformly distributed over the unit interval. We also estimate the discrepancy of the distribution, and we determine the precise order of the counting function of the set of those positive integers n such that ρ (n ) is an integer.
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Published Online: 2005-11-18
Published in Print: 2005-11-18
Walter de Gruyter GmbH & Co. KG
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- Uniform distribution of the fractional part of the average prime divisor
- Analysis of the horizontal Laplacian for the Hopf fibration
- Algebraic inclusions of Moufang polygons
- Topological equivalence of linear representations for cyclic groups: II
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Articles in the same Issue
- Connections on principal bundles over Kähler manifolds with antiholomorphic involution
- Uniform distribution of the fractional part of the average prime divisor
- Analysis of the horizontal Laplacian for the Hopf fibration
- Algebraic inclusions of Moufang polygons
- Topological equivalence of linear representations for cyclic groups: II
- Capacities associated with Dirichlet space on an infinite extension of a local field
- The configuration space of arachnoid mechanisms
