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arXiv · 1808.06285

Adjoint L-functions for GL(3) and U(2,1)

Joseph Hundley·Qing Zhang
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Abstract

We show that the finite part of the adjoint $L$ function (including contributions from all nonarchimedean places, including ramified places) is holomorphic in $\Re(s) \ge 1/2$ for a cuspidal automorphic representation of $GL_3$ over a number field. This improves the main result of [H16]. We obtain more general results for twisted adjoint $L$ functions of both $GL_3$ and quasisplit unitary groups. For unitary groups, we explicate the relationship between poles of twisted adjoint $L$ functions, endoscopy, and the structure of the stable base change lifting.

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Joseph Hundley, Qing Zhang. 2019-01-09. Adjoint L-functions for GL(3) and U(2,1). https://doi.org/10.1093/imrn%2Frnz125

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