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 ...

Let $f_1, \dots, f_R$ be forms of degree $k_1, \dots, k_R$ in $s$ variables. A generalised version of a conjecture by Artin states that the equations $f_1= \dots=f_R=0$ have a non-trivial $p$-adic solution for all primes ...

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 ...

In this work we investigate conditions under which forms of arbitrary degree represent almost all elements of thin sequences (especially the set of squares). Stronger results are given for forms of degree 3 and 4.

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 ...

Artin’s primitive root conjecture states that for any integer a, neither 0, ±1 nor a perfect square, there exist infinitely many primes p such that a is a primitive root modulo p, or alternatively, such that a generates a ...

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 ...

Finger growth is studied in the first part of the thesis and a method for growth prediction is presented. The effectiveness of the method is validated in several tests. Fingerprint image ...

The most important examples of coarse spaces arise from proper metrics on spaces or from metrisable compactifications. In both cases, the bounded subsets are precisely the relatively compact ones. On the other hand, one ...

This thesis discusses a novel approach for fingerprint feature extraction. A new fingerprint structure has been proposed as a basis for the extraction of extended features. These new features ...