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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 ...
• #### 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 ...
• #### 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, ...