Irrationality of certain p-adic periods for small p
| dc.creator | Calegari, Frank | |
| dc.date | 2004-08-16 | |
| dc.date.accessioned | 2026-07-07T05:11:19Z | |
| dc.date.available | 2026-07-07T05:11:19Z | |
| dc.description | Following Apery's proof of the irrationality of zeta(3), Beukers found an elegant reinterpretation of Apery's arguments using modular forms. We show how Beukers arguments can be adapted to a p-adic setting. In this context, certain functional equations arising from Eichler integrals are replaced by the notion of overconvergent p-adic modular forms, and the periods themselves arise not as coefficients of period polynomials but as constant terms of p-adic Eisenstein series. We prove that the analogue of zeta(3) is irrational for p = 2 and 3, as well as the 2-adic analogue of Catalan's constant. | |
| dc.description | Preprint | |
| dc.identifier | https://arxiv.org/abs/math/0408214 | |
| dc.identifier | http://arxiv.org/abs/math/0408214 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72198 | |
| dc.subject | Number Theory | |
| dc.subject | 11F11, 11J72, 11J82 | |
| dc.title | Irrationality of certain p-adic periods for small p | |
| dc.type | text |