Lindelöf hypothesis

Importance: Medium ✭✭
Author(s): Lindelöf, Ernst
Recomm. for undergrads: no
Posted by: porton
on: September 20th, 2010

\begin{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 $\epsilon$, $$\zeta\left(\frac12 + it\right) \mbox{ is }o(t^\varepsilon).$$ \end{conjecture}

\Def{Lindelof hypothesis} in Wikipedia.

Accordingly Wikipedia this hypothesis is implied by Riemann hypothesis.

% You may use many features of TeX, such as % arbitrary math (between $...$ and $$...$$) % \begin{theorem}...\end{theorem} environment, also works for question, problem, conjecture, ... % % Our special features: % Links to wikipedia: \Def {mathematics} or \Def[coloring]{Graph_coloring} % General web links: \href [The On-Line Encyclopedia of Integer Sequences]{}


% Example: %*[B] Claude Berge, Farbung von Graphen, deren samtliche bzw. deren ungerade Kreise starr sind, Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg Math.-Natur. Reihe 10 (1961), 114. % %[CRS] Maria Chudnovsky, Neil Robertson, Paul Seymour, Robin Thomas: \arxiv[The strong perfect graph theorem]{math.CO/0212070}, % Ann. of Math. (2) 164 (2006), no. 1, 51--229. \MRhref{MR2233847} % % (Put an empty line between individual entries)

* indicates original appearance(s) of problem.