Automorphic forms and cubic twists of elliptic curves
| dc.creator | Lieman, Daniel | |
| dc.date | 1994-07-12 | |
| dc.date.accessioned | 2026-07-07T09:15:08Z | |
| dc.date.available | 2026-07-07T09:15:08Z | |
| dc.description | This paper surveys the connection between the elliptic curve E_D: x^3 + y^3 = D and a certain metaplectic form on the cubic cover of GL(3) which has the property that its m,n^{th} Whittaker--Fourier coefficient is essentially the L--series of the curve E_{m^2n}. One may obtain information about the collective behavior the curves E_D by exploiting this connection; for example, one can prove: Theorem: Fix any prime p \ne 3, and any congruence class c mod p. Then there are infinitely many D congruent to c mod p such that the curve E_D has no rational solutions. This paper is fairly self-contained; no prior knowledge of algebraic number theory, analytic number theory or metaplectic forms is assumed. On the other hand, this paper is a survey, no proofs are included. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/9407202 | |
| dc.identifier | http://arxiv.org/abs/math/9407202 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152918 | |
| dc.subject | Number Theory | |
| dc.subject | Representation Theory | |
| dc.title | Automorphic forms and cubic twists of elliptic curves | |
| dc.type | text |