Zeros of ζ″(s) & ζ‴(s) in σ < 1/2

Abstract

There is only one pair of non-real zeros of ζ″(s), and of ζ‴(s), in the left half-plane. The Riemann Hypothesis implies that ζ″(s) and ζ‴(s) have no zeros in the strip 0 ≤ ℜs < 1/2. 19991 Mathematics Subject Classification. Primary 11M26. © TÜBİTAK.