Abstract
In this paper, we outline the Hecke theory for Hermitian modular forms in the sense of Hel Braun for arbitrary class number of the attached imaginary-quadratic number field. The Hecke algebra turns out to be commutative. Its inert part has a structure analogous to the case of the Siegel modular group and coincides with the tensor product of its p-components for inert primes p. This leads to a characterization of the associated Siegel-Eisenstein series. The proof also involves Hecke theory for particular congruence subgroups.
Dedicated to Murugesan Manickam on the occasion of his 60th birthday.
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Hauffe-Waschbüsch, A., Krieg, A. (2020). On Hecke Theory for Hermitian Modular Forms. In: Ramakrishnan, B., Heim, B., Sahu, B. (eds) Modular Forms and Related Topics in Number Theory. ICNT 2018. Springer Proceedings in Mathematics & Statistics, vol 340. Springer, Singapore. https://doi.org/10.1007/978-981-15-8719-1_6
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