Proof of a conjecture of Keith on congruences of the reciprocal of a false theta function

Abstract: Recently, Keith investigated reciprocals of false theta functions and proved some interesting results such as congruences, asymptotic bounds, and combinatorial identities. At the end of his paper, Keith posed a conjecture on congruences modulo 4 and 8 for the coefficients of the reciprocal of a false theta function. In this paper, we not only confirm Keith's conjecture, but also prove a generalized result.