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On relation between asymptotic and Abel densities

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Abstract A natural method how to measure sets of natural numbers is the asymptotic density which is a special case of weighted densities. These densities are based on the Riesz… Click to show full abstract

Abstract A natural method how to measure sets of natural numbers is the asymptotic density which is a special case of weighted densities. These densities are based on the Riesz summation method. A completely different approach is the Abel summation method. This leads to the concept of the Abel density. In this paper we prove estimates of the values of the lower and upper Abel densities, depending on values of the lower and upper asymptotic densities.

Keywords: abel; method; relation asymptotic; asymptotic abel; abel densities

Journal Title: Journal of Number Theory
Year Published: 2020

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