TY - JOUR
T1 - Zeroes of partial sums of the zeta-function
AU - Platt, David J
AU - Trudgian, Timothy
PY - 2016/2/29
Y1 - 2016/2/29
N2 - This article considers the positive integers N for which ζN(s)=∑Nn=1n−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 N there are infinitely many such zeroes.
AB - This article considers the positive integers N for which ζN(s)=∑Nn=1n−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 N there are infinitely many such zeroes.
KW - 11M06 (primary)
KW - 11Y35 (secondary)
U2 - 10.1112/S1461157015000340
DO - 10.1112/S1461157015000340
M3 - Article
VL - 19
SP - 37
EP - 41
JO - LMS Journal of Computation and Mathematics
JF - LMS Journal of Computation and Mathematics
SN - 1461-1570
IS - 1
ER -