Thesis (doctoral)--Friedrich-Wilhelms-Universität zu Berlin, 1932. / "Sonderabdruck aus den "Schriften des Mathematischen Seminars und des Instituts für angewandte Mathematik der Universität Berlin" Band 1"--T.p. verso. Vita. Includes bibliographical references.

Thesis--Amsterdam. / "Stellingen" inserted. Includes bibliographical references (p. [259]-263).

Thesis (M.S.)--Youngstown State University, 2009. / Includes index. Also available via the World Wide Web in PDF format.

This dissertation contains a number of results on properties of infinite algebraic extensions of the rational field, all of which have a view toward the study of heights in diophantine geometry. We investigate whether subextensions of extensions generated by roots of polynomials of a given degree are themselves generated by polynomials of small degree, a problem motivated by the study of heights. We discuss a relative version of the Bogomolov property (the absence of small points) for extensions of fields of algebraic numbers. We describe the relationship between the Bogomolov property and the structure of the multiplicative group. Finally, we describe some results on height lower bounds which can be interpreted as diophantine approximation results in the multiplicative group. / text

published_or_final_version / Mathematics / Master / Master of Philosophy

Not available / text

In this thesis, we investigate modularity of elliptic curves over a general totally real number field, establishing a finiteness result for the set non-modular j-invariants. By analyzing quadratic points on some modular curves, we show that all elliptic curves over certain real quadratic fields are modular. / Mathematics

published_or_final_version / Mathematics / Master / Master of Philosophy

No description available.

No description available.