2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62152We present a compact formula computing rational trigonometric sums. E. Verlinde's expression for the dimension of conformal blocks in WZW theory is an example of such a sum. As an application, we show that a formula of Bismut and Labourie for the Riemann-Roch numbers of moduli spaces of flat connections on a Riemann surface coincides with Verlinde's expression.34 pagesCombinatoricsHigh Energy Physics - TheoryAlgebraic GeometryA residue theorem for rational trigonometric sums and Verlinde's formulatext