Blättern Fakultät für Mathematik und Informatik (inkl. GAUSS) nach "Blomer, Valentin Prof. Dr." Betreuer
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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, ...