Lindelöf Hypothesis

The Lindelöf hypothesis is a conjecture about the rate of growth of the Riemann zeta function on the critical line that is implied by the Riemann Hypothesis.

It says that, for any $$\epsilon > 0$$:


 * $$\forall \epsilon > 0: \zeta \left({\frac 1 2 + it}\right) \text{ is }\mathcal{O}(t^\epsilon),$$

as $$t \to \infty$$ (see Big O-notation).

Since $$\epsilon$$ can always be replaced by a smaller value, we can also write the conjecture as:


 * $$\forall \epsilon > 0: \zeta \left({\frac 1 2 + it}\right) \text{ is } o(t^\epsilon)$$

as $$t \to \infty$$ (see Little O-notation).