A Kloosterman sum in a relative trace formula for 𝐺𝐿₄

Ye, Yangbo

doi:10.1090/S1088-4165-98-00049-1

A Kloosterman sum in a relative trace formula for $GL_4$
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Represent. Theory 2 (1998), 370-392 Request permission

Abstract:

We study a Kloosterman sum for $GL_4$ and prove that it is equal to an exponential sum over a quadratic number field. This identity has applications in a relative trace formula for $GL_4$ which might be used to give a new proof of quadratic base change and characterize its image.

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