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.
- 11M06 (primary)
- 11Y35 (secondary)