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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnm144, 39 pages, doi:10.1093/imrn/rnm144 published on February 5, 2008
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Copyright © The Author 2008. Published by Oxford University Press.

The Voronoi Formula for GL(n, R)

Dorian Goldfeld1 and Xiaoqing Li2,

1 Department of Mathematics, Columbia University, New York, NY 10027, USA
2 Department of Mathematics, College of Arts and Sciences, University at Buffalo, The State University of New York Buffalo, NY 14260-2900, USA

Correspondence: Correspondence to be sent to: xl29{at}buffalo.edu

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 Formula for all n ≥ 3.

Communicated by Prof. Jim Cogdell


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