Browsing Fakultät für Mathematik und Informatik (inkl. GAUSS) by Referee "Mihailescu, Preda Prof. Dr."
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Cyclotomic Norm Diophantine Equations
(20231025)In this thesis, I consider two Diophantine norm equations. For the equation of the NagellLjunggren equation $\frac{x^p1}{x1} = p^e y^q$ 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_pextension and the cyclotomic Z_pextension
(20210415)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 ... 
Two Cases of Artin's Conjecture
(20210225)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 nontrivial $p$adic solution for all primes ... 
The BarbanDavenportHalberstam for tuples of kfree numbers
(20201023)An asymptotic formula for variance of tuples of kfree numbers in arithmetic progressions 
The split prime μconjecture and further topics in Iwasawa theory
(20190325)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 μconjecture for abelian extensions of imaginary quadratic fields. In Chapter ... 
Exakte Moduln über dem von Manuel Köhler beschriebenen Ring
(20181113)When proving an equivariant universal coefficient theorem for C*Algebras acted on by a finite cyclic group Z/pZ, Manuel Köhler introduces the endomorphism ring R of the tuple (C,C(G),D). The aim of this thesis is to show ... 
Diophantine Representation in Thin Sequences
(20160824)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. 
Fourier and Variational Based Approaches for Fingerprint Segmentation
(20150522)Fingerprint recognition plays an important role in many commercial applications and is used by millions of people every day, e.g. for unlocking mobile phones. Fingerprint image segmentation is typically the first processing ... 
A new approach to the investigation of Iwasawa invariants
(20150105)Let K be a fixed number field, let p be a prime number, and let Z_p denote the additive group of padic integers. The growth of the pSylow subgroups of the ideal class groups of the intermediate fields in a Z_pextension ... 
Statistical Inference for Propagation Processes on Complex Networks
(20140729)Scientists of various research fields have discovered the advantages of networkcentric analysis, which captures complex systems by networks and allows for their representation as a collection of nodes connected by links. ... 
On Artin's primitive root conjecture
(20140715)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 ... 
A unified framework for spline estimators
(20130709)This dissertation develops a uni ed framework to study the (asymptotic) properties of all (periodic) spline based estimators, that is of regression, penalized and smoothing splines. The explicit form of the periodic ... 
Cryptanalysis of the Fuzzy Vault for Fingerprints: Vulnerabilities and Countermeasures
(20130708)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
(20120410)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 ... 
Fingerprint Growth Prediction, Image Preprocessing and Multilevel Judgment Aggregation
(20110106)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 ... 
Julia Set as a Martin Boundary
(20101118)The Julia set of the class of hyperbolic rational maps having a totally disconnected Julia set is here identified as the Martin boundary of a Markov chain by using symbolic dynamics. When ... 
Some Aspects on Coarse Homotopy Theory
(20100108)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 ... 
Twisted Kloosterman sums and cubic exponential sums
(20091215)In this thesis work, we study the problem of the distribution of cubic exponential sums. Using the theory of of automorphic forms, we are able to determine the asymptotic behavior of these ... 
Hierarchically linked extended features for fingerprint processing
(20090323)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 ... 
Modelling and Analysing Orientation Fields of Fingerprints
(20070921)Global features of fingerprints, the most useful of which are orientation fields, are deployed for classification, image enhancement, and to define intrinsic coordinates. We thus strive for ...