Olivia Beckwith

activity

20242026

collaborators

5 papers

math.NT2026

A modular framework for generalized Hurwitz class numbers I

Olivia Beckwith, Andreas Mono

We discover a non-trivial relation between the mock modular generating functions of the level $1$ and level $N$ Hurwitz class numbers. This relation yields a holomorphic modular fo…

math.NT2025

Scarcity of partition congruences on semiprime progressions

Scott Ahlgren, Olivia Beckwith

In recent work with Raum the authors considered congruences for the ordinary partition function $p (n)$ of the form $p (ℓ Q^{r} n + I^^{2}) \equiv 0 (mod ℓ)$ where $ℓ, Q \geq 5$ are pri…

math.NT2025

Summation formulas for Hurwitz class numbers and other mock modular coefficients

Olivia Beckwith, Nikolaos Diamantis, Rajat Gupta +2

We prove a formula for weighted sums of the first $n$ coefficients of mock modular forms of moderate growth and apply it to Hurwitz class numbers and coefficients of negative half…

math.NT2024

A modular framework for generalized Hurwitz class numbers II

Olivia Beckwith, Andreas Mono

In a recent preprint, we constructed a sesquiharmonic Maass form $G$ of weight $\frac{1}{2}$ and level $4 N$ with $N$ odd and squarefree. Extending seminal work by Duke, I…

math.NT2024

Holomorphic projection for sesquiharmonic Maass forms

Michael Allen, Olivia Beckwith, Vaishavi Sharma

We study the holomorphic projection of mixed mock modular forms involving sesquiharmonic Maass forms. As a special case, we numerically express the holomorphic projection of a func…