The decomposition formula for Verlinde Sums
Annales de l'Institut Fourier, Online first, 42 p.

We prove a decomposition formula for Verlinde sums (rational trigonometric sums), as a discrete counterpart to the Boysal–Vergne decomposition formula for Bernoulli series. Motivated by applications to fixed point formulas in Hamiltonian geometry, we develop differential form valued version of Bernoulli series and Verlinde sums, and extend the decomposition formula to this wider context.

Nous prouvons une formule de décomposition des sommes de Verlinde (sommes rationnelles trigonométriques), comme contrepartie discrète de la formule de décomposition de Boysal–Vergne pour les séries de Bernoulli. Motivés par des applications aux formules à point fixe en géométrie hamiltonienne, nous développons une version à valeur dans les formes différentielles des séries de Bernoulli et des sommes de Verlinde, et nous étendons la formule de décomposition à ce contexte plus général.

Received:
Revised:
Accepted:
Online First:
DOI: 10.5802/aif.3511
Classification: 40B99,  53D30
Keywords: Verlinde sums, rational trigonometric sums, Bernoulli series
Loizides, Yiannis 1; Meinrenken, Eckhard 2

1 Cornell University Dept. of Mathematics 310 Malott Hall Ithaca, NY 14853 (USA)
2 University of Toronto Dept. of Mathematics 40 St. George St. Toronto, ON, M5S 2E4 (Canada)
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Loizides, Yiannis; Meinrenken, Eckhard. The decomposition formula for Verlinde Sums. Annales de l'Institut Fourier, Online first, 42 p.

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