eprintid: 19157
rev_number: 14
eprint_status: archive
userid: 1992
dir: disk0/00/01/91/57
datestamp: 2015-07-30 08:23:36
lastmod: 2015-10-15 07:33:16
status_changed: 2015-07-30 08:23:36
type: doctoralThesis
metadata_visibility: show
creators_name: Bermudez Tobon, Yamidt
title: An efficient algorithm to compute an elliptic
curve from a corresponding function field
automorphic form
subjects: ddc-510
divisions: i-110400
adv_faculty: af-11
abstract: Elliptic modular forms of weight 2 and elliptic modular curves are strongly related. In the rank-2 Drinfeld module situation, we have still modular curves that can be described analytically through Drinfeld modular forms. 
Gekeler and Reversat prove how the results of Drinfeld can be used to construct the analytic uniformization of the elliptic curve attached to a given automorphic
form. Longhi, building on ideas of Darmon, defines a multiplicative integral that theoretically allows to find the corresponding Tate parameter. In this thesis we develop and present a polynomial time algorithm to compute
the integral proposed by Longhi. Also we devised a method to find a rational equation of the corresponding representative for the isogeny class.
date: 2015
id_scheme: DOI
id_number: 10.11588/heidok.00019157
ppn_swb: 1658253884
own_urn: urn:nbn:de:bsz:16-heidok-191572
date_accepted: 2015-07-23
advisor: HASH(0x55a9a64e7d00)
language: eng
bibsort: BERMUDEZTOANEFFICIEN2015
full_text_status: public
citation:   Bermudez Tobon, Yamidt  (2015) An efficient algorithm to compute an elliptic curve from a corresponding function field automorphic form.  [Dissertation]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/19157/1/Version%20final%20para%20imprimir.pdf