On the integrality of modular functions over $\mathbb{Z}[j]$ and Kronecker-type congruences

Ho Yun Jung, Ja Kyung Koo, Dong Hwa Shin

Let $N$ be a positive integer and let $f$ be a meromorphic modular function of level $N$ with rational Fourier coefficients. For a prime $p$, define a function $f_p$ on the complex…