Mathematische Zeitschrift

, Volume 279, Issue 1–2, pp 267–270 | Cite as

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

  • Shunsuke Yamana


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


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

Mathematics Subject Classification

11F66 11F70 



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.


  1. 1.
    Arthur, J., Clozel, L.: Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula, Ann. of Math. Studies 120, Princeton Univ. Press, Princeton, N.J., (1989)Google Scholar
  2. 2.
    Bump, D., Ginzburg, D.: Spin \(L\)-functions on symplectic groups. Int. Math. Res. Not. 8, 153–160 (1992)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Bump, D., Ginzburg, D.: Spin \(L\)-functions on \(\text{ GSp }_{8}\) and \(\text{ GSp }_{10}\). Trans. Am. Math. Soc. 352(2), 875–899 (1999)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Ginzburg, D.: On spin \(L\)-functions for orthogonal groups. Duke Math. J. 77, 753–798 (1995)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Ginzburg, D.: On standard \(L\)-functions for \(E_6\) and \(E_7\). J. Reine Angew Math. 465, 101–131 (1995)Google Scholar
  6. 6.
    Ginzburg, D., Rallis, S.: The exterior cube \(L\)-function for GL(6). Compos. Math. 123, 243–272 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Hundley, J.: Spin \(L\)-functions for \(\text{ GSO }_{10}\) and \(\text{ GSO }_{12}\). Israel J. Math. 165, 103–132 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Ikeda, T.: On the location of poles of the triple L-functions. Compos. Math. 83, 187–237 (1992)zbMATHGoogle Scholar
  9. 9.
    Kim, H.: On local \(L\)-functions and normalized intertwining operators. Canad. J. Math. 57(3), 535–597 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Shahidi, F.: On certain \(L\)-functions. Am. J. Math. 103, 297–355 (1981)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Faculty of MathematicsKyushu UniversityFukuokaJapan

Personalised recommendations