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- W4382134975 abstract "Grönwall's function (G) is defined for all natural numbers (n>1) by (G(n)=frac{sigma(n)}{n cdot log log n}) where (sigma(n)) is the sum of the divisors of (n) and (log) is the natural logarithm. We require the properties of extremely abundant numbers, that is to say left to right maxima of (n mapsto G(n)). We also use the colossally abundant and hyper abundant numbers. There are several statements equivalent to the famous Riemann hypothesis. We state that the Riemann hypothesis is true if and only if there exist infinitely many pairs ((N,N')) of consecutive colossally abundant numbers (N< N') such that (G(N)< G(N')). Using this new criterion, we prove that the Riemann hypothesis is true." @default.
- W4382134975 created "2023-06-27" @default.
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- W4382134975 date "2023-06-26" @default.
- W4382134975 modified "2023-10-18" @default.
- W4382134975 title "Riemann Hypothesis on Grönwall's Function" @default.
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- W4382134975 doi "https://doi.org/10.32388/zjnvf8.8" @default.
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