Joshua Males

Asymptotics for $d$ -fold partition diamonds and related infinite products

Kathrin Bringmann, William Craig, Joshua Males

We prove an asymptotic formula for the number of $d$ -fold partition diamonds of $n$ and their Schmidt-type counterparts. In order to do so, we study the asymptotic behavior of cert…

Crank equidistribution and $(k, j)$ -overlined partitions

Adithya Chakravarthy, Joshua Males, Shuyang Shen

In a paper published in 2023, Wagner introduced and studied Jacobi forms with complex multiplication, and gave several applications. One such application was in constructing a new…

math.CO2023

A note on the equidistribution of $3$ -colour partitions

Joshua Males

In this short note, we prove equidistribution results regarding three families of three-colour partitions recently introduced by Schlosser and Zhou. To do so, we prove an asymptoti…

Central $L$ -values of newforms and local polynomials

Joshua Males, Andreas Mono, Larry Rolen +1

In this paper, we characterize the vanishing of twisted central $L$ -values attached to newforms of square-free level in terms of certain polynomials of quadratic forms introduced b…

Oscillating asymptotics and conjectures of Andrews

Amanda Folsom, Joshua Males, Larry Rolen +1

In 1986, Andrews studied the function $σ (q)$ from Ramanujan's ``Lost" Notebook, and made several conjectures on its Fourier coefficients $S (n)$ , which count certain partition ranks…

Jensen polynomials associated with Wright's circle method: Hyperbolicity and Turán inequalities

Jashan Bal, Fern Haraldson, Joshua Males +1

We study the Fourier coefficients of functions satisfying a certain version of Wright's circle method with finitely many major arcs. We show that the Jensen polynomials associated…

Equidistribution and partition polynomials

Amanda Folsom, Joshua Males, Larry Rolen

Using equidistribution criteria, we establish divisibility by cyclotomic polynomials of several partition polynomials of interest, including $s pt$ -crank, overpartition pairs, and $…

Sign changes in statistics for plane partitions

Walter Bridges, Johann Franke, Joshua Males

Recent work of Cesana, Craig and the third author shows that the trace of plane partitions is asymptotically equidistributed in residue classes mod $b$ . Applying a technique of the…

Exact formulae and Turán inequalities for Vafa-Witten invariants of $K 3$ surfaces

Daniel R. Johnston, Joshua Males

We consider three different families of Vafa-Witten invariants of $K 3$ surfaces. In each case, the partition function that encodes the Vafa-Witten invariants is given by combinatio…

The second shifted difference of partitions and its applications

Kevin Gomez, Joshua Males, Larry Rolen

A number of recent papers have estimated ratios of the partition function $p (n - j) / p (n)$ , which appears in many applications. Here, we prove an easy-to-use effective bound on these…

Asymptotics, Turán inequalities, and the distribution of the BG-rank and 2-quotient rank of partitions

Andrew Baker, Joshua Males

Let $j, n$ be even positive integers, and let $p_{j} (n)$ denote the number of partitions with BG-rank $j$ , and $p_{j} (a, b; n)$ to be the number of partitions with B…

Asymptotic equidistribution for partition statistics and topological invariants

Giulia Cesana, William Craig, Joshua Males

We provide a general framework for proving asymptotic equidistribution, convexity, and log concavity of coefficients of generating functions on arithmetic progressions. Our central…

Distributions on partitions arising from Hilbert schemes and hook lengths

Kathrin Bringmann, William Craig, Joshua Males +1

Recent works at the interface of algebraic combinatorics, algebraic geometry, number theory, and topology have provided new integer-valued invariants on integer partitions. It is n…

math.NT2021★ 1 cited

Local Maaß forms and Eichler--Selberg type relations for negative weight vector-valued mock modular forms

Joshua Males, Andreas Mono

By comparing two different evaluations of a modified (à la Borcherds) higher Siegel theta lift on even lattices of signature $(r, s)$ , we prove Eichler--Selberg type relations for a…

Higher Siegel theta lifts on Lorentzian lattices, harmonic Maass forms, and Eichler-Selberg type relations

Joshua Males

We investigate so-called "higher" Siegel theta lifts on Lorentzian lattices in the spirit of Bruinier-Ehlen-Yang and Bruinier-Schwagenscheidt. We give a series representation of th…

Bivariate asymptotics for eta-theta quotients with simple poles

Giulia Cesana, Joshua Males

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 $…