  We study the fluctuation of the number of particles in ideal Bose-Einstein
condensates, both within the canonical and the microcanonical ensemble.
Employing the Mellin-Barnes transformation, we derive simple expressions that
link the canonical number of condensate particles, its fluctuation, and the
difference between canonical and microcanonical fluctuations to the poles of a
Zeta function that is determined by the excited single-particle levels of the
trapping potential. For the particular examples of one- and three-dimensional
harmonic traps we explore the microcanonical statistics in detail, with the
help of the saddle-point method. Emphasizing the close connection between the
partition theory of integer numbers and the statistical mechanics of ideal
Bosons in one-dimensional harmonic traps, and utilizing thermodynamical
arguments, we also derive an accurate formula for the fluctuation of the number
of summands that occur when a large integer is partitioned.
