Cercles de remplissage for the Riemann Zeta Function

http://dx.doi.org/10.4153/CMB-2003-009-3
Canad. Math. Bull. 46(2003), 95-97

  Published:2003-03-01
 Printed: Mar 2003

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.