Browsing Fakultät für Mathematik und Informatik (inkl. GAUSS) by Advisor "Mihailescu, Preda Prof. Dr."

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    • Cyclotomic Norm Diophantine Equations 

      Chen, Han (2023-10-25)
      In this thesis, I consider two Diophantine norm equations. For the equation of the Nagell-Ljunggren equation $\frac{x^p-1}{x-1} = p^e y^q$ with distinct odd prime exponents $p, q$, I show that, for $p > 3$, it has no ...

    • Classical Conjectures in Iwasawa Theory for the split prime Z_p-extension and the cyclotomic Z_p-extension 

      Müller, Katharina (2021-04-15)
      This thesis constist of three parts. The first one considers the so called split prime Z_p extension over an imaginary quadratic field in which the rational prime p splits. In this setup we discuss the mu=0 conjecture as ...

    • The split prime μ-conjecture and further topics in Iwasawa theory 

      Crisan, Vlad-Cristian (2019-03-25)
      The thesis is divided in three independent chapters, each focused on a different problem in Iwasawa theory. In Chapter 1 we prove the split prime μ-conjecture for abelian extensions of imaginary quadratic fields. In Chapter ...

    • Diophantine Equations and Cyclotomic Fields 

      Bartolomé, Boris (2016-03-09)
      This thesis examines some approaches to address Diophantine equations, specifically we focus on the connection between the Diophantine analysis and the theory of cyclotomic fields. First, we propose a quick introduction ...

    • A new approach to the investigation of Iwasawa invariants 

      Kleine, Sören (2015-01-05)
      Let K be a fixed number field, let p be a prime number, and let Z_p denote the additive group of p-adic integers. The growth of the p-Sylow subgroups of the ideal class groups of the intermediate fields in a Z_p-extension ...

    • Cryptanalysis of the Fuzzy Vault for Fingerprints: Vulnerabilities and Countermeasures 

      Tams, Berend-Benjamin (2013-07-08)
      The fuzzy fingerprint vault is a popular approach to protect a fingerprint's minutiae as a building block of a security application. In this thesis simulations of several attack scenarios are conducted against implementations ...

    • The Capitulation Problem in Class Field Theory 

      Bembom, Tobias (2012-04-10)
      We develop Chevalley's Theorem and interesting implications. Revisiting Galois Cohomology we analyse the structure of the capitulation kernel. Moreover investigate the growth of ideal classes and consequences of a ...