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)
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Susan L Pywell (Manager), Simon A Burbidge (Other), Polly E Eccleston (Other) & Simon H Atack (Other)