Frequent 'dirichlet-series+ca.classical-analysis-and-odes+inequalities' Questions

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Can one show $\left|\frac{2(\zeta'(x))^2-\zeta''(x)\zeta(x)}{\zeta^3(x)}\right|\leq \frac{2}{(x-\frac{1}{2})^2}$ for $x\in\mathbb{R}\cap [1,\infty)$?

I have found that $\left|\frac{2(\zeta'(x))^2-\zeta''(x)\zeta(x)}{\zeta^3(x)}\right|\leq \frac{2}{(x-\frac{1}{2})^2}$ for all real $x$ such that $x>1$ seems to be true. I have plotted the ...

Haidara

asked Nov 3 at 13:07

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Can one show $\left|\frac{2(\zeta'(x))^2-\zeta''(x)\zeta(x)}{\zeta^3(x)}\right|\leq \frac{2}{(x-\frac{1}{2})^2}$ for $x\in\mathbb{R}\cap [1,\infty)$?

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Can one show $\left|\frac{2(\zeta'(x))^2-\zeta''(x)\zeta(x)}{\zeta^3(x)}\right|\leq \frac{2}{(x-\frac{1}{2})^2}$ for $x\in\mathbb{R}\cap [1,\infty)$?

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