The decomposition formula for Verlinde Sums

TL;DR

This paper establishes a decomposition formula for Verlinde sums, linking them to Bernoulli series, and extends this to differential forms motivated by Hamiltonian geometry applications.

Contribution

It introduces a decomposition formula for Verlinde sums and generalizes it to differential forms, bridging discrete sums and geometric applications.

Findings

Proved a decomposition formula for Verlinde sums.

Extended the formula to differential form valued versions.

Facilitated applications in Hamiltonian geometry.

Abstract

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.