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

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


Publications referenced by this paper.

Conformal characters and the modular representation

  • P. Bántay, T. Gannon
  • JHEP 0602
  • 2006
Highly Influential
7 Excerpts

Vector-valued modular forms and Poincaré series

  • M. Knopp, G. Mason
  • Illinois J. Math. 48
  • 2004
3 Excerpts

The kernel of the modular group representation and the Galois action in RCFT

  • P. Bántay
  • Comm. Math. Phys. 233
  • 2003
1 Excerpt

Modular functions and Dirichlet series in number theory

  • T. M. Apostol
  • 2nd edn, Springer, New York
  • 1990
1 Excerpt

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