Abstract
We describe Hecke operators on Manin symbols over imaginary quadratic fields. As by-product we obtain a form of universal L-series associated with eigenforms.
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Acknowledgements
The present article is extracted from the author dissertation which was supervised by Gabor Wiese. The author thanks him for his time, teaching and support from the start until the completion of this work. The author wishes to thank John Cremona and Mehmet Haluk Sengün for the various discussions. This work started as one of the FP6 European Research Training Networks “Galois Theory and Explicit Methods” projects (GTEM; MRTN-CT-2006-035495); I acknowledge their financial support. Finally, I would like to express my gratitude to the referee for his careful reading, constructive comments and suggestions.
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Mohamed, A. (2014). Universal Hecke L-Series Associated with Cuspidal Eigenforms over Imaginary Quadratic Fields. In: Böckle, G., Wiese, G. (eds) Computations with Modular Forms. Contributions in Mathematical and Computational Sciences, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-319-03847-6_9
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DOI: https://doi.org/10.1007/978-3-319-03847-6_9
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