Lindelöf hypothesis

Importance: Medium ✭✭
Author(s): Lindelöf, Ernst
Recomm. for undergrads: no
Posted by: porton
on: September 20th, 2010
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 $, $$\zeta\left(\frac12 + it\right) \mbox{ is }o(t^\varepsilon).$$

Lindelof hypothesis in Wikipedia.

Accordingly Wikipedia this hypothesis is implied by Riemann hypothesis.


* indicates original appearance(s) of problem.