Some explicit aspects of modular formsover imaginary quadratic eldsDissertation presented in partial ful llment ofthe requirements for the degree of Dr. rer. nat.byAdam Mohamedfrom Ouani, Anjouan, ComorosatUniversit at Duisburg-Essen,Faculty of Mathematics, Campus EssenEssen, June 2011Doctoral Committee:Prof. Dr. Gabor Wiese Dr. John Cremona.Date of oral examination: 13:09:2011DeclarationBy submitting this thesis, I declare that the entirety of the work contained therein is myown, original work, that I am the owner of the copyright thereof (unless to the extentexplicitly otherwise stated) and that I have not previously in its entirety or in partsubmitted it for obtaining any quali cation.Date: June 2011Copyright © Adam MohamedAll rights reservedAcknowledgmentsI would like to express my profound gratitude to my supervisor Prof. Dr. Gabor Wiese,without whom this work would not have been in this present form. He introduces meto theory of modular forms, and other related subjects. I am grateful for his patience,teaching, help, time and insightful suggestions during the course of this work.I am very grateful to Prof. Dr. John Cremona for accepting to referee this dissertation.This work started as one of the FP6 European Research Training Networks \GaloisTheory and Explicit Methods" project (GTEM; MRTN-CT-2006-035495 ), I gratefullyacknowledge their nancial support.
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