Matthew Boylan

collaborators

3 papers

math.NT2026

Indices of nilpotency in certain spaces of modular forms

Matthew Boylan, Swati

We study the index of nilpotency relative to certain Hecke operators in spaces of modular forms with integer weight and level $N$ with integer coefficients modulo primes $p$ for $(…

math.NT2026

Congruence properties modulo prime powers for a class of partition functions

Matthew Boylan, Swati

Let $p$ be prime, and let $p_{[1, p]} (n)$ denote the function whose generating function is $\prod (1 - q^{n})^{- 1} (1 - q^{p n})^{- 1}$ . This function and its generalizations $p_{[c^{\ell}…

math.NT2025

Explicit images for the Shimura Correspondence

Matthew Boylan, Swati

In 2014, Yang showed that for $F \in A_{r, s, 1, 1_{N}}$ , we have $Sh_{r} (F ∣ V_{24}) = G \otimes I ¨ _{12}$ where $G\in S^{new}_{r+2s - 1}(Î_{0}(6), - \left( \f…