# On p-adic decomposable form inequalities

 Title: On p-adic decomposable form inequalities Author: Liu, Junjiang Publisher: Mathematics Department (MI), Faculty of Science, Leiden University Issue Date: 2015-03-05 Keywords: Number TheoryDiophantine approximation(p-adic) Decomposable form inequality Abstract: The main concern of this thesis is the number of the solutions $N_F(m)$ of Decomposable form inequalities $F(x) \leq m$. In 2001, Thunder proved a conjecture of W.M. Schmidt, stating that, under suitable finiteness conditions, one has $N_F(m) \ll m^{n/d}$ where the implicit constant depends only on $n$ and $d$. The results in this thesis extend Thunder’s various results on Decomposable form inequalities to the p-adic setting (See Chapters 2, 4 and 5). In Chapter 3, we also show the effectivity of the condition under which the number of solutions of p-adic decomposable form inequalities is finite. Description: Promotor: Peter Stevenhagen, Jan-Hendrik Evertse, Co-promotor: Pascal AutissierWith summaries in French and Dutch Faculty: Faculteit der Wiskunde en Natuurwetenschappen Citation: Liu, J., 2015, Doctoral thesis, Leiden University Handle: http://hdl.handle.net/1887/32076

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Introduction 291.1Kb View/Open
Summary in French longer version 290.7Kb View/Open
Chapter 1 350.4Kb View/Open
Chapter 2 370.7Kb View/Open
Chapter 3 320.2Kb View/Open
Chapter 4 351.0Kb View/Open
Chapter 5 446.7Kb View/Open
Bibliography 158.4Kb View/Open
Abstract 225.6Kb View/Open
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Summary in French 225.9Kb View/Open
Acknowledgements_Curriculum Vitae 99.58Kb View/Open
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