paper

A monotonicity property of Riemann's xi function and a reformulation of the Riemann Hypothesis

arXiv:1005.1104 · doi:10.1007/s10998-010-1037-3

Abstract

We prove that Riemann's xi function is strictly increasing (respectively, strictly decreasing) in modulus along every horizontal half-line in any zero-free, open right (respectively, left) half-plane. A corollary is a reformulation of the Riemann Hypothesis.

4 pages, published version

A monotonicity property of Riemann's xi function and a reformulation of the Riemann Hypothesis · wovepaper