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Note on the Riemann Hypothesis
[post]

2022
unpublished

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 $\prod_{q\leq q_{n}}\left(1+\frac{1}{q} \right) >\frac{e^{\gamma}}{\zeta(2)}\times \log\theta(q_{n})$ is satisfied for all primes $q_{n}> 3$, where $\theta(x)$ is the Chebyshev function, $\gamma\approx 0.57721$ is

doi:10.33774/coe-2022-r1vjx-v2
fatcat:crvoy2b3cjdb7fo3t4mgohgmci