Now showing items 1-14 of 14

• #### A new approach to the investigation of Iwasawa invariants ﻿

(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 ...
• #### 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 ...
• #### 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 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.
• #### Explicit GL(2) trac formulas and uniform, mixed Weyl laws ﻿

(2012-10-24)
This thesis provides an explicit, general trace formula for the Hecke and Casimir eigenvalues of GL(2)-automorphic representations over a global field. In special cases, we obtain Selberg's original trace formula. Computations ...
• #### 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 ...
• #### On Artin's primitive root conjecture ﻿

(2014-07-15)
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 ...
• #### 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.
• #### The Barban-Davenport-Halberstam for tuples of k-free numbers ﻿

(2020-10-23)
An asymptotic formula for variance of tuples of k-free numbers in arithmetic progressions
• #### The Capitulation Problem in Class Field Theory ﻿

(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 ...
• #### 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, ...