Authors: Stević, Stevo 
Affiliations: Mathematics 
Mathematical Institute
Title: On integer parts of the reciprocal remainders of some sums
Journal: Journal of Inequalities and Applications
Volume: 2022
Issue: 1
First page: 139
Issue Date: 2022
Rank: ~M21a
ISSN: 1025-5834
DOI: 10.1186/s13660-022-02879-w
Abstract: 
We present generalizations of some results on the integer parts of the reciprocal remainders of the zeta function ζ(s) with s= 2 and s= 3 , and a very short and elegant proof of a recent result on the integer parts of the reciprocal remainders of the series ζ(3). We also give some historical and theoretical remarks to problems of this type, conduct some analyses, and make some connections with the theory of linear difference equations with constant coefficients.
Keywords: Asymptotics | Closed-form formula | Integer part | Linear difference equations | Remainder of a sum
Publisher: Springer Link

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