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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn058, 15 pages, doi:10.1093/imrn/rnn058 published on June 10, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

Trilinear Forms and Triple Product Epsilon Factors

Wee Teck Gan

Mathematics Department, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA

Correspondence: Correspondence to be sent to: wgan{at}math.ucsd.edu

We give a short and simple proof of a theorem of Dipendra Prasad on the existence or nonexistence of invariant trilinear forms on a triple of irreducible representations of GL2(F) or Dx, where $F$ is a nonarchimedean local field of zero or odd characteristic and $D$ is the unique quaternion division F-algebra. The answer is controlled by the central value of the triple product epsilon factor. Our proof works uniformly for all representations and without restriction on residual characteristic. It also gives an analogous theorem for any separable cubic F-algebra.



References

  1. Garrett P. Decomposition of Eisenstein series: Rankin triple products. Annals of Mathematics (1987) 125(2):209–35.[CrossRef][ISI]
  2. Harris M., Kudla S. On a Conjecture of Jacquet. In: Contributions to Automorphic Forms, Geometry, and Number Theory—Hida H., Ramakrishnan D., Shahidi F., eds. (2004) Baltimore, MD: Johns Hopkins University Press. 355–71.
  3. Ikeda T. On the location of poles of the triple L-functions. Compositio Mathematicae (1992) 83(2):187–237.
  4. Kudla S., Rallis S. Ramified degenerate principal series representations for Sp(n). Israel Journal of Mathematics (1992) 78(2–3):209–56.[CrossRef][ISI]
  5. Prasad D. Trilinear forms for representations of GL(2) and local epsilon factors. Compositio Mathematicae (1990) 75:1–46.
  6. Prasad D. Invariant linear forms for representations of GL(2) over a local field. American Journal of Mathematics (1992) 114:1317–63.[CrossRef][ISI]
  7. Prasad D. "Relating invariant linear form and local epsilon factors via global methods," with an appendix by H. Saito. Duke Journal of Mathematics (2007) 138(2):233–61.[CrossRef]
  8. Prasad D., Schulze-Pillot R. Generalised form of a conjecture of Jacquet, and a local consequence. Journal Reine Angew Math (2008) 616:219–36.
  9. Piatetski-Shapiro I., Rallis S. Rankin triple L functions. Compositio Mathematicae (1987) 64(1):31–115.
  10. Ramakrishnan D. Modularity of the Rankin-Selberg L-series, and multiplicity one for SL(2). Annals of Mathematics (2000) 152(1):45–111.[CrossRef][ISI]

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This Article
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