An orthogonality relation for a thin family of $GL(3)$ Maass forms

preprint2015arXivOpen access

We prove an orthogonality relation for the Fourier-Whittaker coefficients of a thin family of $GL(3)$ Maass forms containing all self-dual forms. This is obtained by analysing the Kuznetsov trace formula on $GL(3)$ for a certain family of test functions. The method also yields Weyl's law for the same family of Maass forms.

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An orthogonality relation for a thin family of $GL(3)$ Maass forms

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An orthogonality relation for a thin family of GL(3)GL(3)GL(3) Maass forms

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An orthogonality relation for a thin family of $GL(3)$ Maass forms