  We study the survival probability for long times in an open spherical
billiard, extending previous work on the circular billiard. We provide details
of calculations regarding two billiard configurations, specifically a sphere
with a circular hole and a sphere with a square hole. The constant terms of the
long-term survival probability expansions have been derived analytically. Terms
that vanish in the long time limit are investigated analytically and
numerically, leading to connections with the Riemann hypothesis.
