On a Result of Atkin and Lehner
| dc.creator | Carlton, David | |
| dc.date | 1999-03-22 | |
| dc.date.accessioned | 2026-07-07T05:28:25Z | |
| dc.date.available | 2026-07-07T05:28:25Z | |
| dc.description | We wish to give a new proof of one of the main results of Atkin and Lehner. Their theory depends, among other things, on a theorem characterizing forms in S_k(Gamma_0(N)) whose Fourier coefficients satisfy a certain vanishing condition. Our proof involves rephrasing this vanishing condition in terms of representation theory; this, together with an elementary linear algebra argument, allows us to rewrite the problem as a collection of local problems. Furthermore, the classical phrasing of the theorem makes the resulting local problems trivial; this is in contrast to the method of Casselman, whose local problem relies upon knowledge of the structure of irreducible representations of GL_2(Q_p). Our proof is therefore much more accessible to mathematicians who aren't specialists in the representation theory of p-adic groups; the method is also applicable to other Atkin-Lehner-style problems. | |
| dc.description | 6 pages | |
| dc.identifier | https://arxiv.org/abs/math/9903131 | |
| dc.identifier | http://arxiv.org/abs/math/9903131 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78254 | |
| dc.subject | Number Theory | |
| dc.subject | 11F11 | |
| dc.title | On a Result of Atkin and Lehner | |
| dc.type | text |