6 papers
Moments of partition statistics, Bell polynomials and Eisenstein-type series
Soon-Yi Kang, Byungchan Kim, Chanhee Lee
We develop a systematic method to express generating functions for moments of combinatorial statistics in terms of partition traces. We employ an algebraic approach based on the co…
On the Alexander polynomials of modular knots
Soon-Yi Kang, Toshiki Matsusaka, Kyungbae Park
Closed geodesics associated with indefinite binary quadratic forms, or equivalently with real quadratic irrationals, have long been studied as geometric …
Hecke equivariance of the divisor map
Daeyeol Jeon, Soon-Yi Kang, Chang Heon Kim +1
We study the multiplicative Hecke operators acting on the space of meromorphic modular forms, and show that the divisor map to divisors on is a Hecke equivariant map. As a…
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…
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 . Our main theorem unifies various results from the literature,…
Hauptmoduln and even-order mock theta functions modulo 2
Soon-Yi Kang, Seonkyung Kim, Toshiki Matsusaka +1
The Fourier coefficients of the elliptic modular -function are always even for . In contrast, for , it is conjectured that…