Further properties of a function of Ogg and Ligozat
| dc.creator | Castano-Bernard, Carlos | |
| dc.date | 2006-03-01 | |
| dc.date.accessioned | 2026-07-07T07:06:24Z | |
| dc.date.available | 2026-07-07T07:06:24Z | |
| dc.description | Certain identities of Ramanujan may be succinctly expressed in terms of the rational function w_N(g) = w_N(f) - 1/w_N(f) on the modular curve X_0(N), where f is a certain modular unit on the Nebentypus cover X_χ(N) introduced by Ogg and Ligozat for N prime congruent to 1 (mod 4) and w_N is the Fricke involution. These correspond to levels N = 5, 13, where the genus of X_0(N) is zero. In this paper we produce some analogs of these identities for each w_N(g) such that X_0(N) has genus 1, 2, and also for each h = g + w_N(g) such that the Atkin-Lehner quotient X_0+(N) has genus 1, 2. We also found that if n is the degree of the field of definition F of the non-trivial zeros of the latter, then the degree of the normal closure of F over Q is the n-th solution of Singmaster's Problem. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0603016 | |
| dc.identifier | http://arxiv.org/abs/math/0603016 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110015 | |
| dc.subject | Number Theory | |
| dc.subject | 11G16; 11R04 | |
| dc.title | Further properties of a function of Ogg and Ligozat | |
| dc.type | text |