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- W4226323980 abstract "The Riemann Hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part $frac{1}{2}$. In 2011, Sol{'e} and and Planat stated that the Riemann Hypothesis is true if and only if the Dedekind inequality $prod_{qleq q_{n}}left(1+frac{1}{q} right)>frac{e^{gamma}}{zeta(2)}timeslogtheta(q_{n})$ is satisfied for all primes $q_{n}>3$, where $theta(x)$ is the Chebyshev function, $gammaapprox 0.57721$ is the Euler-Mascheroni constant and $zeta(x)$ is the Riemann zeta function. We can deduce from that paper, if the Riemann Hypothesis is false, then the Dedekind inequality is not satisfied for infinitely many prime numbers $q_{n}$. Using this result, we prove the Riemann Hypothesis is true when $(1-frac{0.15}{log^{3}x})^{frac{1}{x}}times x^{frac{1}{x}}geq 1+frac{log(1-frac{0.15}{log^{3}x})+log x}{x}$ is always satisfied for every sufficiently large positive number $x$. However, we know that inequality is trivially satisfied for every sufficiently large positive number $x$. In this way, we show the Riemann Hypothesis is true." @default.
- W4226323980 created "2022-05-05" @default.
- W4226323980 creator A5039521075 @default.
- W4226323980 date "2022-04-25" @default.
- W4226323980 modified "2023-09-24" @default.
- W4226323980 title "Note on the Riemann Hypothesis" @default.
- W4226323980 doi "https://doi.org/10.33774/coe-2022-r1vjx-v5" @default.
- W4226323980 hasPublicationYear "2022" @default.
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