Soon-Yi Kang

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20242026

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math.NT2024

Quasi-modularity in MacMahon partition variants and prime detection

Soon-Yi Kang, Toshiki Matsusaka, Gyucheol Shin

Building on the results of Craig, van Ittersum, and Ono, we provide a refined understanding of MacMahon's partition functions and their variants, including their quasi-modular prop…

math.NT2024

A unified approach to Rohrlich-type divisor sums

Daeyeol Jeon, Soon-Yi Kang, Chang Heon Kim +1

We propose a systematic method for analyzing Rohrlich-type divisor sums for arbitrary congruence subgroups $Γ_{0} (N)$ . Our main theorem unifies various results from the literature, a…

math.NT2024

Hauptmoduln and even-order mock theta functions modulo 2

Soon-Yi Kang, Seonkyung Kim, Toshiki Matsusaka +1

The Fourier coefficients $c_{1} (n)$ of the elliptic modular $j$ -function are always even for $n \neq \equiv 7 (mod 8)$ . In contrast, for $n \equiv 7 (mod 8)$ , it is conjectured that…