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# Cercles de remplissage for the Riemann Zeta Function

Published:2003-03-01
Printed: Mar 2003
• P. M. Gauthier
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## Abstract

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: cercles de remplissage, Riemann zeta function
 MSC Classifications: 30 - unknown classification 30