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Can one show $h(x)=|2(\zeta'(x))^2-\zeta''(x)\zeta(x)|$ is a decreasing function for $x\in\mathbb{R}\cap [1,\infty)$?
This question is related to This question.
When I tried to approach it I couldn't even proof that the LHS is a decreasing function on the given domain using regular methods. I have tried to write the ...
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Are $\zeta'(0)$ and $\beta'(0)$ algebraic numbers?
Let $\zeta$ be the Riemann zeta function and $\beta$ the Dirichlet beta function. We know that $\zeta (0)=-1/2$ and $\beta (0)=1/2$ are algebraic numbers over $\mathbb{Q}$. This led me to the ...
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