| dc.contributor.advisor |
Vaaler , Jeffrey D . |
|
| dc.contributor.committeeMember |
Voloch , Felipe |
|
| dc.contributor.committeeMember |
Ciperiani , Mirela |
|
| dc.contributor.committeeMember |
Helm , David |
|
| dc.contributor.committeeMember |
Petsche , Clayton |
|
| dc.creator |
Fili , Paul Arthur |
|
| dc.date.accessioned |
2010 -10 -20T20 :45 :45Z |
|
| dc.date.accessioned |
2010 -10 -20T20 :45 :50Z |
|
| dc.date.accessioned |
2011 -08 -16T15 :48 :04Z |
|
| dc.date.available |
2010 -10 -20T20 :45 :45Z |
|
| dc.date.available |
2010 -10 -20T20 :45 :50Z |
|
| dc.date.available |
2011 -08 -16T15 :48 :04Z |
|
| dc.date.created |
2010 -05 |
|
| dc.date.issued |
2010 -10 -20 |
|
| dc.date.submitted |
May 2010 |
|
| dc.identifier.uri |
http : / /hdl .handle .net /2152 /ETD -UT -2010 -05 -1416 |
|
| dc.description.abstract |
We introduce decompositions determined by Galois field and degree of the space of algebraic numbers modulo torsion and the space of algebraic points on an elliptic curve over a number field . These decompositions are orthogonal with respect to the natural inner product associated to the L² Weil height recently introduced by Allcock and Vaaler in the case of algebraic numbers and the inner product naturally associated to the Néron -Tate canonical height on an elliptic curve . Using these decompositions , we then introduce vector space norms associated to the Mahler measure . For algebraic numbers , we formulate L[superscript p] Lehmer conjectures involving lower bounds on these norms and prove that these new conjectures are equivalent to their classical counterparts , specifically , the classical Lehmer conjecture in the p=1 case and the Schinzel -Zassenhaus conjecture in the p=[infinity] case . |
|
| dc.format.mimetype |
application /pdf |
|
| dc.language.iso |
eng |
|
| dc.subject |
Algebraic numbers |
|
| dc.subject |
Weil height |
|
| dc.subject |
Mahler measure |
|
| dc.subject |
Lehmer's problem |
|
| dc.title |
Orthogonal decompositions of the space of algebraic numbers modulo torsion |
|
| dc.type.genre |
thesis |
* |
| dc.type.material |
text |
* |
| thesis.degree.name |
Doctor of Philosophy |
|
| thesis.degree.level |
Doctoral |
|
| thesis.degree.discipline |
Mathematics |
|
| thesis.degree.grantor |
University of Texas at Austin |
|
| thesis.degree.department |
Mathematics |
|
| dc.date.updated |
2010 -10 -20T20 :45 :50Z |
|