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Abstract

This thesis consists of two main parts. In the first part an integral transform between spaces of nonstandard test functions on the affine space of dimension n is constructed. The integral transform satisfies a summation formula of Poisson type, which is derived from an analogue of the Arthur--Selberg trace formula for the Lie algebra of n-by-n matrices. In the second part a proof of Conjecture 9.12 of Braverman--Kazhdan in their article "gamma-functions of representations and lifting" on the acyclicity of their l-adic gamma-sheaves over certain affine spaces is given for GL(n).

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