Asymptotic equidistribution for partition statistics and topological invariants

Giulia Cesana; William Craig; Joshua Males

doi:10.1016/j.jnt.2023.10.007

Asymptotic equidistribution for partition statistics and topological invariants

Giulia Cesana
, William Craig
, Joshua Males

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

2 Citations (Scopus)

4 Downloads (Pure)

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 proven 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
of a certain scheme central in work of Göttsche.

Original language	English
Pages (from-to)	373-396
Number of pages	24
Journal	Journal of Number Theory
Volume	256
Early online date	24 Nov 2023
DOIs	https://doi.org/10.1016/j.jnt.2023.10.007
Publication status	Published - 1 Mar 2024

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© 2023 Elsevier Inc.

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https://arxiv.org/abs/2111.13766

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AU - Craig, William

AU - Males, Joshua

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N2 - 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 proven 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 of a certain scheme central in work of Göttsche.

AB - 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 proven 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 of a certain scheme central in work of Göttsche.

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DO - 10.1016/j.jnt.2023.10.007

M3 - Article (Academic Journal)

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SP - 373

EP - 396

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Asymptotic equidistribution for partition statistics and topological invariants

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