Corrigendum to ``The holomorphic flow of the Riemann zeta function''

Abstract

Theorem 4.5 of [2], describing the topological type of the zeros of the flow ṡ = ζ(s) at reflected points off the critical line, claiming they were the same, contains an error. We gratefully acknowledge Professor Cevat Gokcek for pointing out the error to us. In some circumstances the types will never be the same. Indeed, it appears to be unlikely that a fixed formal relationship will exist between the types of flow for ζ(s) at reflected points off the critical line. Given that such points are not at hand (and expected not to be found), examples are currently impossible to come by. The revised statement and proof are given below. Some proof reading errors picked up by a helpful referee are also noted. Let Φ(s) = π−s/2Γ( s 2 ),