Modular invariance, modular identities and supersingular j-invariants
| dc.creator | Milas, Antun | |
| dc.date | 2005-12-28 | |
| dc.date | 2006-09-06 | |
| dc.date.accessioned | 2026-07-07T06:55:48Z | |
| dc.date.available | 2026-07-07T06:55:48Z | |
| dc.description | To every $k$-dimensional modular invariant vector space we associate a modular form on $SL(2,\mathbb{Z})$ of weight $2k$. We explore number theoretic properties of this form and find a sufficient condition for its vanishing which yields modular identities (e.g., Ramanujan-Watson's modular identities). Furthermore, we focus on a family of modular invariant spaces coming from suitable two-dimensional spaces via the symmetric power construction. In particular, we consider a two-dimensional space spanned by graded dimensions of certain level one modules for the affine Kac-Moody Lie algebra of type $D_4^{(1)}$. In this case, the reduction modulo prime $p=2k+3 \geq 5$ of the modular form associated to the $k$-th symmetric power classifies supersingular elliptic curves in characteristic $p$. This construction also gives a new interpretation of certain modular forms studied by Kaneko and Zagier. | |
| dc.description | Final version, 16 pages, AMS-LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0512606 | |
| dc.identifier | http://arxiv.org/abs/math/0512606 | |
| dc.identifier | Math. Res. Lett. 13, (2006) 729-746 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106404 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Number Theory | |
| dc.title | Modular invariance, modular identities and supersingular j-invariants | |
| dc.type | text |