The Voronoi Formula for GL(n, ℝ)

A Voronoi formula is an identity A=B where A is a weighted sum over Fourier coefficients of an automorphic form and B is another weighted sum involving the Fourier coefficients of the dual automorphic form. The weights in A are additive characters multiplied by a test function while the weights in B are Kloosterman sums multiplied by a suitable transform of the test function. We derive an explicit Voronoi formula for even Maass forms in $\mathcal{L}^2(SL(n,\hspace{0.4em}\mathbb{Z})\backslash GL(n,\hspace{0.4em}\mathbb{R})/O(n,\hspace{0.4em}\mathbb{R})\hspace{0.4em}\cdot\hspace{0.4em}\mathbb{R}^\times)$ for all n≥3.