Asymptotic equidistribution for partition statistics and topological invariants

2021/11/26 by Cesana, Giulia, Craig, William, Males, Joshua
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2111.13766

Abstract

We provide a general framework for proving asymptotic equidistribution, convexity, and log concavity 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.

Related

• Sign changes in statistics for plane partitions
• A note on hook length equidistribution on arithmetic progressions
• Topology of Z₃ equivariant Hilbert schemes
• On Fourier asymptotics and effective equidistribution
• Distributions on partitions arising from Hilbert schemes and hook lengths