Automorphic forms on Feit’s Hermitian lattices. (English) Zbl 1487.11047
“We consider the genus of 20 classes of unimodular Hermitian lattices of rank 12 over the Eisenstein integers. This set is the domain for a certain space of algebraic modular forms. We find a basis of Hecke eigenforms, and guess global Arthur parameters for the associated automorphic representations, which recover the computed Hecke eigenvalues. Congruences between Hecke eigenspaces, combined with the assumed parameters, recover known congruences for classical modular forms, and support new instances of conjectured Eisenstein congruences for \(\mathbb{U}(2,2)\) automorphic forms.”
In short, I found the article to be very good and useful. I hope it will be used by researchers.
In short, I found the article to be very good and useful. I hope it will be used by researchers.
Reviewer: M. A. Dehghani (Yazd)
MSC:
| 11F55 | Other groups and their modular and automorphic forms (several variables) |
| 11E39 | Bilinear and Hermitian forms |
Keywords:
automorphic representations of unitary groups; unimodular Hermitian lattices; algebraic modular forms; congruences of automorphic formsReferences:
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