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arXiv · 1911.03157

On Hecke theory for Hermitian modular forms

Adrian Hauffe-Waschbüsch·Aloys Krieg
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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.

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Adrian Hauffe-Waschbüsch, Aloys Krieg. 2020-10-08. On Hecke theory for Hermitian modular forms. https://doi.org/10.1007/978-981-15-8719-1_6

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