The Riemann hypothesis and an upper bound of the divisor function for odd integers

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In [6] Robin showed that the Riemann hypothesis is equivalent to the statement that Robin's inequality sigma (n) < e(gamma) n log log n holds for n >= 5041, where gamma is the Euler-Mascheroni constant. We provide a sharper bound for sigma (n) than Robin's one for integers, by using the ideas of Choie et al. [1], and show that Robin's inequality holds for n not equivalent to 0 (mod 3) with finitely many exceptions.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2015-01
Language
English
Article Type
Article
Keywords

VALUES

Citation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, v.421, no.1, pp.917 - 924

ISSN
0022-247X
DOI
10.1016/j.jmaa.2014.07.063
URI
http://hdl.handle.net/10203/195805
Appears in Collection
MA-Journal Papers(저널논문)
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