Speiser's criterion

A. Speiser (Math Annahlen 110 (1934) 514-521) proved that the Riemann Hypothesis is equivalent to the non-vanishing of the derivative $\zeta'(s)$ in the left-half of the critical strip $0<\sigma< 1/2.$ Levinson and Montgomery [MR 54 #5135] gave an alternative, quantitative version of this result which led to Levinson's [MR 58 #27837] discovery of his method for counting zeros on the critical line. He then proceeded to prove that at least 1/3 of the zeros of $\zeta(s)$ are on the critical line.

Back to the main index for The Riemann Hypothesis.