A monotonicity property of Riemann’s xi function and a reformulation of the Riemann hypothesis
Copyright policy ) Jonathan Sondow; Cristian Dumitrescu;
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.
4 pages, published version
11M26, Mathematics - Number Theory, FOS: Mathematics, Number Theory (math.NT)
11M26, Mathematics - Number Theory, FOS: Mathematics, Number Theory (math.NT)
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).8 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
citations
Citations provided by BIP!
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
Citations provided by BIP!popularityPopularity provided by BIP!
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
Popularity provided by BIP! 8
Average
Top 10%
Average
Green
bronze
Fields of Science