zeta


Lindelöf hypothesis ★★

Author(s): Lindelöf

\begin{conjecture} For any $\epsilon>0$ $$\zeta\left(\frac12 + it\right) \mbox{ is }\mathcal{O}(t^\epsilon).$$

Since $\epsilon$ can be replaced by a smaller value, we can also write the conjecture as, for any positive $\epsilon$, $$\zeta\left(\frac12 + it\right) \mbox{ is }o(t^\varepsilon).$$ \end{conjecture}

Keywords: Riemann Hypothesis; zeta

The Riemann Hypothesis ★★★★

Author(s): Riemann

The zeroes of the Riemann zeta function that are inside the Critical Strip (i.e. the vertical strip of the complex plane where the real part of the complex variable is in ]0;1[), are actually located on the Critical line ( the vertical line of the complex plane with real part equal to 1/2)

Keywords: Millenium Problems; zeta

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