Eungang Cho

Petersson-Rigid Lattices in a Census of 100 Rank-Three Root Bases

The first paper worked out one family of four lattices in full — |det| = 12, 24, 36and 72. This paper generalizes it. We enumerate the 44 symmetrizable rank-threehyperbolic Cartan matrices and their 56 depth-one edits, 100 root bases in all, andcompute the obstruction space S_{5/...

Petersson-Rigid Lattices in a Census of 100 Rank-Three Root Bases

The first paper worked out one family of four lattices in full — |det| = 12, 24, 36and 72. This paper generalizes it. We enumerate the 44 symmetrizable rank-threehyperbolic Cartan matrices and their 56 depth-one edits, 100 root bases in all, andcompute the obstruction space S_{5/...

Forced Shadows of an Obstructed Hyperbolic Kac–Moody Denominator

The four orders of the quaternion algebra B6 carry four reflective wall data on lattices of signature (3,2); three integrate to Borcherds denominators and one is obstructed. The failed denominator survives as a weakly harmonic Maass form, and we prove its shadow is a Hecke eigenf...

Forced Shadows of an Obstructed Hyperbolic Kac–Moody Denominator

The four orders of the quaternion algebra B6 carry four reflective wall data on lattices of signature (3,2); three integrate to Borcherds denominators and one is obstructed. The failed denominator survives as a weakly harmonic Maass form, and we prove its shadow is a Hecke eigenf...