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An extended large sieve for Maaß cusp forms

dc.contributor.advisorBlomer, Valentin Prof. Dr.
dc.contributor.authorHäußer, Christoph Renatus Ulrich
dc.titleAn extended large sieve for Maaß cusp formsde
dc.contributor.refereeBlomer, Valentin Prof. Dr.
dc.description.abstractengFor 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 families of Maaß cusp forms for the Hecke congruence subgroup of odd prime level N with respect to Dirichlet characters of the modulus of the level. The result hinges on a suitable version of the Bruggeman- Kuznetsov formula, upon which we build our argument, proving in a first step an asymptotic formula for a weighted L^2 sum, featuring the Fourier coefficients of the functions from the family we consider. The inequality we finally conclude in the main theorem, describes an upper bound for this weighted L^2 sum, that in general does not meet the expectation from theoretical considerations of the large
dc.contributor.coRefereeBrüdern, Jörg Prof. Dr.
dc.subject.englarge sievede
dc.subject.engMaaß cusp formsde
dc.subject.engnumber theoryde
dc.affiliation.instituteFakultät für Mathematik und Informatikde
dc.subject.gokfullMathematik (PPN61756535X)de

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