Zeroes of partial sums of the zeta-function

David J. Platt; Timothy S. Trudgian

doi:10.1112/S1461157015000340

Zeroes of partial sums of the zeta-function

David J. Platt, Timothy S. Trudgian

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

This article considers the positive integers N for which ζ_N(s) = ^N_n=1 n^-s has zeroes in the half-plane R(s) > 1. Building on earlier results, we show that there are no zeroes for 1 ≤ N ≤18 and for N = 20,21,28. For all other there are infinitely many such zeroes.

Original language	English
Pages (from-to)	37-41
Number of pages	5
Journal	LMS Journal of Computation and Mathematics
Volume	19
Issue number	1
DOIs	https://doi.org/10.1112/S1461157015000340
Publication status	Published - 1 Jan 2016

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abstract = "This article considers the positive integers N for which ζN(s) = Nn=1 n-s has zeroes in the half-plane R(s) > 1. Building on earlier results, we show that there are no zeroes for 1 ≤ N ≤18 and for N = 20,21,28. For all other there are infinitely many such zeroes.",

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AB - This article considers the positive integers N for which ζN(s) = Nn=1 n-s has zeroes in the half-plane R(s) > 1. Building on earlier results, we show that there are no zeroes for 1 ≤ N ≤18 and for N = 20,21,28. For all other there are infinitely many such zeroes.

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Zeroes of partial sums of the zeta-function

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