Swati

collaborators

5 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.NT2026

Repellent properties of perfect powers on partition functions: a heuristic approach

Summer Haag, Praneel Samanta, Swati +3

In 2013, Sun conjectured that the partition function $p (n)$ is never a perfect power for $n \geq 2$ . Building on this, Merca, Ono, and Tsai recently observed that for any fixed int…

math.NT2025

Exceptional Congruences for Eta-quotient newforms

Eddie O'Sullivan, Henry Stone, Swati +1

In 1973, Swinnerton-Dyer completely classified all congruences for coefficients of normalized eigenforms in weights $k \in {12, 16, 18, 20, 22, 26}$ on $Î_{0}(1) = \operatorname…

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…