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Now showing items 1-14 of 14

    • A new approach to the investigation of Iwasawa invariants 

      Kleine, Sören (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 

      Häußer, Christoph Renatus Ulrich (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 

      Waibel, Fabian (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 

      Möser, Rebecca Ulrike (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 

      Dumke, Jan Henrik (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 

      Baur, Stefan (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 

      Palm, Marc (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 

      Balakci, Deniz (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 

      Ambrose, Christopher Daniel (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 

      Helfrich, Lutz (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 

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

      Bembom, Tobias (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 

      Dehnert, Fabian (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 

      Topacogullari, Berke (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, ...