  Lagarias and Rhoades generalized harmonic Maass forms by considering forms
which are annihilated by a number of iterations of the action of the
xi-operator. In our previous work, we considered polyharmonic weak Maass forms
by allowing the exponential growth at cusps, and constructed a basis of the
space of such forms. This paper focuses on the case of half-integral weight. We
construct a basis as an analogue of our work, and give arithmetic formulas for
the Fourier coefficients in terms of traces of CM values and cycle integrals of
polyharmonic weak Maass forms. These results put the known results into a
common framework.
