A monotonicity property of Riemann’s xi function and a reformulation of the Riemann hypothesis
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.
Key words and phrasescritical line critical strip functional equation gamma function Hadamard product horizontal half-line open half-plane increasing in modulus monotonicity nonreal zero Riemann Hypothesis Riemann zeta function xi function
Mathematics subject classification number11M26
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