  We show that there exists an integrable function on the $n$-sphere $(n\ge
2)$, whose Ces\`aro (C,$\frac{n-1}{2}$) means with respect to the spherical
harmonic expansion diverge unboundedly almost everywhere. By studying
equivalence theorems, we also obtain the corresponding results for Riesz and
Bochner-Riesz means. This extends results of Stein (1961) for flat tori and
complements the work of Taibleson (1985) for spheres.
