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# Vector-valued modular functions for the modular group and the hypergeometric equation

@inproceedings{Bntay2007VectorvaluedMF, title={Vector-valued modular functions for the modular group and the hypergeometric equation}, author={Peter B{\'a}ntay and Terry Gannon}, year={2007} }

- Published 2007
DOI:10.4310/CNTP.2007.v1.n4.a2

A general theory of vector-valued modular functions, holomorphic in the upper half-plane, is presented for finite-dimensional representations of the modular group. This also provides a description of vector-valued modular forms of arbitrary half-integer weight. It is shown that the space of these modular functions is spanned, as a module over the polynomials in J , by the columns of a matrix that satisfies an abstract hypergeometric equation, providing a simple solution of the Riemann–Hilbert… CONTINUE READING