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Cercles de remplissage for the Riemann Zeta Function

Published online by Cambridge University Press:  20 November 2018

P. M. Gauthier
P. M. Gauthier*
Affiliation:
Département de mathématiques et de statistique et Centre de rechèrches mathématiques, Université de Montréal, CP 6128 Centre Ville, Montréal, Québec, H3C 3J7, email: gauthier@dms.umontreal.ca
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Abstract

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The celebrated theorem of Picard asserts that each non-constant entire function assumes every value infinitely often, with at most one exception. The Riemann zeta function has this Picard behaviour in a sequence of discs lying in the critical band and whose diameters tend to zero. According to the Riemann hypothesis, the value zero would be this (unique) exceptional value.

Keywords

30cercles de remplissageRiemann zeta function
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 46 , Issue 1 , 01 March 2003 , pp. 95 - 97
Copyright
Copyright © Canadian Mathematical Society 2003

References

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[4] Titchmarsh, E. C., The theory of the Riemann zeta-function. 2nd edition (ed. D. R. Heath-Brown), Clarendon Press, Oxford University Press, New York, 1986.Google Scholar