On the integer part of the reciprocal of the Riemann zeta function tail at certain rational numbers in the critical strip
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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 .
1947 ◽
Vol 53
(10)
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pp. 976-982
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2007 ◽
Vol 62
(6)
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pp. 251-252
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1983 ◽
Vol 41
(164)
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pp. 759-759
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2012 ◽
Vol 87
(3)
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pp. 452-461
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2018 ◽
Vol 70
(3)
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pp. 831-848
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