On the integer part of the reciprocal of the Riemann zeta function tail at certain rational numbers in the critical strip

We prove that the integer part of the reciprocal of the tail of ζ ( s ) at a rational number s = 1 p for any integer with p ≥ 5 or s = 2 p for any odd integer with p ≥ 5 can be described essentially as the integer part of an explicit quantity corresponding to it. To deal with the case when s = 2 p ,...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2019; no. 1; pp. 1 - 12
Main Authors Hwang, WonTae, Song, Kyunghwan
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 23.10.2019
Springer Nature B.V
SpringerOpen
Subjects
Alliances
Analysis
Applications of Mathematics
Critical strip
Integers
Mathematics
Mathematics and Statistics
Numbers
Riemann zeta function tail
Siegel’s theorem
Siegel’s theorem
11M06
11B83
Riemann zeta function tail
11G30
Critical strip
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Summary:We prove that the integer part of the reciprocal of the tail of ζ ( s ) at a rational number s = 1 p for any integer with p ≥ 5 or s = 2 p for any odd integer with p ≥ 5 can be described essentially as the integer part of an explicit quantity corresponding to it. To deal with the case when s = 2 p , we use a result on the finiteness of integral points of certain curves over Q .
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-019-2230-4