Duke Mathematical Journal

Residue theorem for rational trigonometric sums and Verlinde's formula

András Szenes

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We present a compact formula computing rational trigonometric sums. Such sums appeared in the work of E. Verlinde on the dimension of conformal blocks in Wess-Zumino-Witten (WZW) theory. As an application, we show that a formula of J.-M. Bismut and F. Labourie for the Riemann-Roch numbers of moduli spaces of flat connections on a Riemann surface coincides with Verlinde's expression.

Article information

Duke Math. J., Volume 118, Number 2 (2003), 189-227.

First available in Project Euclid: 23 April 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11L03: Trigonometric and exponential sums, general
Secondary: 14H60: Vector bundles on curves and their moduli [See also 14D20, 14F05] 14N20: Configurations and arrangements of linear subspaces


Szenes, András. Residue theorem for rational trigonometric sums and Verlinde's formula. Duke Math. J. 118 (2003), no. 2, 189--227. doi:10.1215/S0012-7094-03-11821-9. https://projecteuclid.org/euclid.dmj/1082744646

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