Abstract
Abstract
We prove that the integer part of the reciprocal of the tail of $\zeta (s)$
ζ
(
s
)
at a rational number $s=\frac{1}{p}$
s
=
1
p
for any integer with $p \geq 5$
p
≥
5
or $s=\frac{2}{p}$
s
=
2
p
for any odd integer with $p \geq 5$
p
≥
5
can be described essentially as the integer part of an explicit quantity corresponding to it. To deal with the case when $s=\frac{2}{p}$
s
=
2
p
, we use a result on the finiteness of integral points of certain curves over $\mathbb{Q}$
Q
.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
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