We provide a general framework for proving asymptotic equidistribution, convexity, and logconcavity of coefficients of generating functions on arithmetic progressions. Our central tool is a variant of Wright's Circle Method proved by two of the authors with Bringmann and Ono, following work of Ngo and Rhoades. We offer a selection of different examples of such results, proving asymptotic equidistribution results for several partition statistics, modular sums of Betti numbers of two-and three-flag Hilbert schemes, and the number of cells of dimension a (mod b) of a certain scheme central in work of Göttsche.

We employ a variant of Wright's circle method to determine the bivariate asymptotic behaviour of Fourier coefficients for a wide class of eta-theta quotients with simple poles in H.

We employ a variant of Wright’s Circle Method to determine the bivariate asymptotic behavior of Fourier coefficients for a wide class of eta-theta quotients with simple poles in $$\mathbb {H}$$ H .