On Hermitian theta series and modular forms [Elektronische Ressource] / vorgelegt von Michael Hentschel

On Hermitian theta seriesand modular formsMichael Hentschel ⋆ On Hermitian theta series and modular forms„On Hermitian theta seriesand modular forms“Von der Fakultät für Mathematik, Informatik und Naturwissenschaften der RWTH Aachen Uni-versity zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften genehmigteDissertationvorgelegt vonDiplom-MathematikerMichael Hentschelaus Rhede, Kreis BorkenBerichter: Universitätsprofessor Dr. rer. nat. Aloys KriegUniversitätsprofessorin Dr. rer. nat. Gabriele NebeTag der mündlichen Prüfung: 17. Juli 2009Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verfügbar.A few words on the leitmotif of this thesis:The main examples for Hermitian modular forms come from the classical case, from HermitianEisenstein series due to Hel Braun [Br3] or from liftings, see Gritsenko, Ikeda, Krieg, and lotsof others. Cohen and Resnikoff [CoRe] introduced the method of constructing modular formsvia theta-series to the theory of Hermitian modular forms and gave a construction for latticeswhich yield Hermitian modular forms for an arbitrary imaginary quadratic field. In [DeKr]then one finds an elementary method for the construction of those lattices. One is especiallyinterested in the number of distinct isometry classes (in the genus) of lattices which then yielddifferent theta-series, a problem which was already sketched in [CoRe], page 336, ”...its [thegenus] class number remains unknown.”.