Number theoretic properties of Wronskians of Andrews-Gordon series
| dc.creator | Milas, Antun | |
| dc.creator | Mortenson, Eric | |
| dc.creator | Ono, Ken | |
| dc.date | 2005-12-28 | |
| dc.date.accessioned | 2026-07-07T09:33:50Z | |
| dc.date.available | 2026-07-07T09:33:50Z | |
| dc.description | For positive integers $1\leq i\leq k$, we consider the arithmetic properties of quotients of Wronskians in certain normalizations of the Andrews-Gordon $q$-series $$ \prod_{1\leq n\not \equiv 0,\pm i\pmod{2k+1}}\frac{1}{1-q^n}. $$ This study is motivated by their appearance in conformal field theory, where these series are essentially the irreducible characters of $(2,2k+1)$ Virasoro minimal models. We determine the vanishing of such Wronskians, a result whose proof reveals many partition identities. For example, if $P_{b}(a;n)$ denotes the number of partitions of $n$ into parts which are not congruent to $0, \pm a\pmod b$, then for every positive integer $n$ we have $$ P_{27}(12; n)=P_{27}(6;n-1) + P_{27}(3;n-2). $$ We also show that these quotients classify supersingular elliptic curves in characteristic $p$. More precisely, if $2k+1=p$, where $p\geq 5$ is prime, and the quotient is non-zero, then it is essentially the locus of characteristic $p$ supersingular $j$-invariants in characteristic $p$. | |
| dc.description | 13 pages, AMS-LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0512623 | |
| dc.identifier | http://arxiv.org/abs/math/0512623 | |
| dc.identifier | International Journal of Number Theory, 4 (2008), 323-337 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159278 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Number Theory | |
| dc.title | Number theoretic properties of Wronskians of Andrews-Gordon series | |
| dc.type | text |