Lindelöf conjecture, on the behaviour of the Riemann -function
For any ,
It was stated by E. Lindelöf . The Lindelöf conjecture is equivalent to the assertion that for a fixed the number of zeros of that lie in the domain is . The Lindelöf conjecture is therefore a consequence of the Riemann conjecture on the zeros of (cf. Riemann hypotheses). It is known (1982) that
where is a constant such that .
There is a generalization of the Lindelöf conjecture to Dirichlet -functions: For any ,
where is the modulus of the character .
|||E. Lindelöf, "Le calcul des résidus et ses applications à la théorie des fonctions" , Gauthier-Villars (1905)|
|||E.C. Titchmarsh, "The theory of the Riemann zeta-function" , Oxford Univ. Press (1951) pp. Chapt. 13|
|[a1]||A. Ivic, "The Riemann zeta-function" , Wiley (1985)|
Lindelöf hypothesis. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Lindel%C3%B6f_hypothesis&oldid=18908