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.
References
- 1 Ernst Lindelöf: “Quelques remarques sur la croissance de la fonction $\zeta (s)$”. –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 |