Lindelöf hypothesis
From Encyclopedia of Mathematics
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Lindelöf conjecture, on the behaviour of the Riemann -function
For any ,
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It was stated by E. Lindelöf [1]. 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
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where is a constant such that
.
There is a generalization of the Lindelöf conjecture to Dirichlet -functions: For any
,
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where is the modulus of the character
.
References
[1] | E. Lindelöf, "Le calcul des résidus et ses applications à la théorie des fonctions" , Gauthier-Villars (1905) |
[2] | E.C. Titchmarsh, "The theory of the Riemann zeta-function" , Oxford Univ. Press (1951) pp. Chapt. 13 |
Comments
References
[a1] | A. Ivic, "The Riemann zeta-function" , Wiley (1985) |
How to Cite This Entry:
Lindelöf hypothesis. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Lindel%C3%B6f_hypothesis&oldid=23388
Lindelöf hypothesis. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Lindel%C3%B6f_hypothesis&oldid=23388
This article was adapted from an original article by S.M. Voronin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article