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 $\epsilon > 0$:


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

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:


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

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