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Zeroes of partial sums of the zeta-function
Published online by Cambridge University Press: 01 February 2016
Abstract
This article considers the positive integers $N$ for which
${\it\zeta}_{N}(s)=\sum _{n=1}^{N}n^{-s}$ has zeroes in the half-plane
$\Re (s)>1$. Building on earlier results, we show that there are no zeroes for
$1\leqslant N\leqslant 18$ and for
$N=20,21,28$. For all other
$N$ there are infinitely many such zeroes.
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- Research Article
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- © The Author(s) 2016
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