# 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.$\zeta(\frac{1}{2}\!+\!it)\;=\;O(t^{\varepsilon})$  for every  $\varepsilon>0$  when  $t\to\infty$.

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

## References

• 1 Ernst Lindelöf: “Quelques remarques sur la croissance de la fonction $\zeta(s)$”. –Bull. Sci. Math. 32 (1908).
Title Lindelöf hypothesis LindelofHypothesis 2015-08-22 13:08:30 2015-08-22 13:08:30 pahio (2872) pahio (2872) 8 pahio (2872) Conjecture msc 11M06