Abstract

We consider the cohomology group associated with Jacobi cusp forms over Cayley numbers as an example of the general theory of the cohomology groups associated with cusp forms developed by Eichler and Shimura. The theory establishes isomorphisms between the cohomology groups and the vector spaces of vector-valued cusp forms and then expresses their common dimensions in terms of certain geometric invariants in the corresponding quotient spaces. This is an analogue of the Riemann-Roch theorem applied to the cases of vector-valued modular forms.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 811-826
Launched on MUSE
1998-08-01
Open Access
No
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