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

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

2010-05-06

arxiv.org/abs/1005.1104v1

Periodica Mathematica Hungarica 60 (2010) 37-40

Mathematics

Number Theory

4 pages, published version

Scientific paper

10.1007/s10998-010-1037-3

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.

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