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Improving The Adelic Version Of The Minkowski-Hlawka Theorem, Fatmah Alnaser

Graduate Research Theses & Dissertations

In this dissertation we take a method developed by Schmidt to improve the classical version of the Minkowski-Hlawka Theorem and extend that to certain number fields. This leads to an analogous improvement to the adelic Minkowski-Hlawka Theorem in certain cases. We also demonstrate that the adelic version, even in the case where the number field is the field of rational numbers, is more general than the classical version.