Dokumente Fakultät für Mathematik und Informatik (inkl. GAUSS) nach Gutachter "Brüdern, Jörg Prof. Dr."
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An extended large sieve for Maaß cusp forms
(2018-10-18)For a certain big family of Maaß cusp forms, which in a way extends beyond the Hecke congruence subgroup, we establish a large sieve inequality. The set of functions under consideration is constructed by summing specific ... -
Arithmetic and analytical aspects of Siegel modular forms
(2020-09-24)This dissertation treats various topics in the theory of Siegel modular forms on congruence subgroups of large level. In the first part, we compute a second moment of the spinor L-function at the central point and give ... -
Automorphe Formen und L-Funktionen
(2021-03-26)We compute an explicit spectral expansion and deduce an asymptotic formula for the fourth power moment of L-functions associated to a family of characters of a totally real number field with class number 1. In the second ... -
Classical Conjectures in Iwasawa Theory for the split prime Z_p-extension and the cyclotomic Z_p-extension
(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 ... -
Cyclotomic Norm Diophantine Equations
(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 ... -
Diophantine Equations and Cyclotomic Fields
(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 ... -
Diophantine Equations in Many Variables
(2014-11-06)Let K denote a p-adic field and $F_1,..,F_r \in k[x_1, . . . , x_n]$ be forms with respective degrees $d_1, . . . , d_r$. A contemporary version of a conjecture attributed to E. Artin states that $F_1, . . . , F_r$ have a ... -
Diophantine problems over global fields and a conjecture of Artin over function fields
(2023-05-26)This thesis considers three diophantine problems over different global fields and Artin's primitive root conjecture over function fields. In the first chapter, which is a joint project with Christian Bernert, the main ... -
Diophantine problems: inequalities and abelian varieties
(2023-11-10)In this thesis we consider the density of rational points near manifolds and a bound for the torsion on a simple abelian variety of type IV over a number field. In the first part the main result is an asymptotic for the ... -
Diophantine Representation in Thin Sequences
(2016-08-24)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. -
Elliptic curves, modular forms, and the associated exponential sums
(2024-02-27)This thesis focuses on the various arithmetic aspects of elliptic curves and modular forms. Employing the exponential sum estimates obtained from sum-product estimates for finite fields, we estimate exponential sums linked ... -
Fourier expansions of GL(3) Eisenstein series for congruence subgroups
(2016-04-14)In this thesis the Fourier expansions of all types of GL(3) Eisenstein series for the congruence subgroup Gamma_{0}(N) of SL(3)(Z) with N squarefree, are explicitly calculated. Further certain invariance properties of ... -
Quadratische Diophantische Gleichungen über algebraischen Zahlkörpern
(2015-04-23)A search bound for the smallest solution of a quadratic diophantine equation over number fields in at least three variables is established. -
Rational points and lines on cubic hypersurfaces
(2023-10-02)We study the solubility of cubic diophantine equations. In the first chapter, we discuss the convergence of the singular series of a cubic form, which is a central object in the study of the solutions of the associated ... -
The distribution of rational points on some projective varieties
(2020-01-09)This thesis is concerned with establishing Manin's conjecture on the distribution of ratinal points for a certain class of bihomogeneous varieties. It generalizes work of Vaughan on the representation of integers as sum ... -
The shifted convolution of generalized divisor functions
(2017-04-18)We prove an asymptotic formula for the shifted convolution of the divisor functions \(d_k(n)\) and \(d(n)\) with \(k \geq 3\), which is uniform in the shift parameter and which has a power saving error term. Along the way, ... -
The split prime μ-conjecture and further topics in Iwasawa theory
(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 ... -
Two Cases of Artin's Conjecture
(2021-02-25)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 ...