An explicit proof of the weak finite basis theorem and applications to computing ranks of elliptic curves
by Sharon, Zachery A., M.S., THE UNIVERSITY OF TEXAS AT SAN ANTONIO, 2011, 71 pages; 1498638

Abstract:

Let [special characters omitted] be an elliptic curve defined over the field [special characters omitted] of rational numbers, and let [special characters omitted] be the group [special characters omitted] of rational points of [special characters omitted]. The classical proof of Mordell's Weak Finite Basis Theorem shows that [special characters omitted] is finite by embedding it in a certain finite group [special characters omitted] whose genesis is algebraic number-theoretical. Assuming that [special characters omitted] has trivial 2-torsion, we provide an explicit parametrization of [special characters omitted]. This parametrization yields an upper bound for the rank of [special characters omitted] as well as a heuristic algorithm to determine the exact rank. We offer some examples to illustrate the use and limitations of this approach.
 
AdviserEduardo Duenez
SchoolTHE UNIVERSITY OF TEXAS AT SAN ANTONIO
SourceMAI/ 50-01, p. , Sep 2011
Source TypeThesis
SubjectsApplied mathematics; Mathematics
Publication Number1498638
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