On poles of the exterior cube \(L\)-functions for \(\mathrm {GL}_6\)

Abstract

We determine the irreducible cuspidal automorphic representations of \(\mathrm {GL}_6\) whose twisted exterior cube \(L\)-functions have poles.

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Acknowledgments

The author would like to thank Michael Harris for inviting him as a postdoctoral fellow at the Institut de mathématiques de Jussieu, where this paper was written. The research leading to these results has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant agreement no. 290766 (AAMOT). The author is partially supported by JSPS Grant-in-Aid for Research Activity Start-up 24840033.

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Correspondence to Shunsuke Yamana.

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Yamana, S. On poles of the exterior cube \(L\)-functions for \(\mathrm {GL}_6\) . Math. Z. 279, 267–270 (2015). https://doi.org/10.1007/s00209-014-1366-7

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Keywords

  • Exterior cube \(L\)-functions
  • Poles of \(L\)-functions
  • Base change
  • Automorphic induction

Mathematics Subject Classification

  • 11F66
  • 11F70