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Geometry of numbers and exterior algebras: Towards Bombieri--Vaaler's version of Siegel's Lemma
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Perustieteiden korkeakoulu |
Master's thesis
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SCI3054
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en
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50
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Abstract
This thesis provides a study and exploration of the various tools needed to prove Bombieri--Vaaler's version of Siegel's lemma, which focuses on finding integer solutions to a system of linear equations that satisfy a certain bound. The thesis progresses through essential concepts, including lattice packings, Minkowski's convex body theorems, exterior algebras, determinants, rational subspaces, and heights of rational subspaces, while presenting some important examples and results illustrating these concepts. The final theorem of Bombieri--Vaaler's version of Siegel's lemma is an important tool used in transcendental number theory and Diophantine analysis.