Eichler cohomology theorem for vector-valued modular forms (Q2866999)
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scientific article; zbMATH DE number 6236975
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Eichler cohomology theorem for vector-valued modular forms |
scientific article; zbMATH DE number 6236975 |
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10 December 2013
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Eichler cohomology
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vector-valued modular forms
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modular forms
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Eichler cohomology theorem for vector-valued modular forms (English)
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The Eichler cohomology theorem provides a correspondence between modular forms for a discrete subgroup \(\Gamma\) of \(\mathrm{SL}(2, \mathbb R)\) and elements of certain cohomology space of \(\Gamma\). In this paper, given a positive integer \(p\), the author proves the Eichler cohomology theorem for vector-valued modular forms of large weights associated to a representation \(\rho: \mathrm{SL}(2, \mathbb Z) \to \mathrm{GL}(p, \mathbb C)\) of the full modular group \(\mathrm{SL}(2, \mathbb Z)\).
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