Lindelöf hypothesis

Ernst Lindelöf (http://planetmath.org/ernstlindelof) presented in 1908 a conjecture known as Lindelöf hypothesis which concerns the of the Riemann zeta function on the “critical line”  $x=\frac{1}{2}$.  Up to now (2015), this hypothesis has not been proved.  It is weaker than the Riemann hypothesis such that this latter implies it but not conversely.

Lindelöf hypothesis.  $\zeta (\frac{1}{2}+it)=O(t^{\epsilon })$  for every  $\epsilon >0$  when  $t\to \mathrm{\infty }$.

Here $O$ is the Landau big ordo (http://planetmath.org/formaldefinitionoflandaunotation) notation.

Title	Lindelöf hypothesis
Canonical name	LindelofHypothesis
Date of creation	2015-08-22 13:08:30
Last modified on	2015-08-22 13:08:30
Owner	pahio (2872)
Last modified by	pahio (2872)
Numerical id	8
Author	pahio (2872)
Entry type	Conjecture
Classification	msc 11M06