Sihun Jo

The k-Rank Taylor Family: Canonical Harmonic Lifts, Principal Parts, and Rademacher Series

For fixed $k\ge2$, Garvan's modified $k$-rank moments are encoded by odd elliptic Taylor coefficients of an odd-level Appell function. The completed coefficient of order $2n+1$ has weight $2n+3/2$, so the family cannot be realized as a fixed-weight vector-valued modular form. Nevertheless, all non-holomorphic parts ari...