All Questions

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 ...

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

Problem : Show that : $$\frac{1}{\zeta(3)}<2C-1$$ Where we can see the zeta function and the Catalan's constant . After a bounty on Maths Stack Exchange there is no satisfying answer . See https://...

Consider the exponentiated Riemann-Zeta function $\zeta(s)^p$. If it is represented as $$\zeta(s)^p = \sum_{n=1}^\infty\frac{a_n}{n^s}$$ Is there any upper bound we can put on $|a_n|$ in terms of ...

I am currently studying the following inequality involving the square of the modulus of a specific Dirichlet polynomial: $$\left( \sum_{1}^{N}\frac{1}{n} \right)^2 \ \ - \ \left| \sum_{1}^{N}\frac{(...

After getting stuck with the previous positivity (it probably sounds too complex), I would like to give a version of the problem which is of most interest to me. Consider a sequence of real numbers $...