Lindelöf hypothesis

Ernst Lindelöf ( presented in 1908 a conjecture known as Lindelöf hypothesis which concerns the of the Riemann zeta functionDlmfDlmfMathworldPlanetmath on the “critical line”  x=12.  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.ζ(12+it)=O(tε)  for every  ε>0  when  t.

Here O is the Landau big ordo ( notation.


  • 1 Ernst Lindelöf: “Quelques remarques sur la croissance de la fonction ζ(s)”. –Bull. Sci. Math. 32 (1908).
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