Orthogonal decompositions of the space of algebraic numbers modulo torsion

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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 2014 -02 -19T22 :42 :19Z
dc.date.available 2010 -10 -20T20 :45 :45Z
dc.date.available 2010 -10 -20T20 :45 :50Z
dc.date.available 2014 -02 -19T22 :42 :19Z
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

Citation

Orthogonal decompositions of the space of algebraic numbers modulo torsion. Doctoral dissertation, University of Texas at Austin. Available electronically from http : / /hdl .handle .net /2152 /ETD -UT -2010 -05 -1416 .

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