Periods and nonvanishing of central L-values for GL(2n)

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Abstract

Let π be a cuspidal automorphic representation of PGL(2n) over a number field F, and η the quadratic idèle class character attached to a quadratic extension E/F. Guo and Jacquet conjectured a relation between the nonvanishing of L(1/2, π)L(1/2, π ⊗ η) for π of symplectic type and the nonvanishing of certain GL(n,E) periods. When n = 1, this specializes to a well-known result of Waldspurger. We prove this conjecture, and related global results, under some local hypotheses using a simple relative trace formula. We then apply these global results to obtain local results on distinguished supercuspidal representations, which partially establish a conjecture of Prasad and Takloo-Bighash.

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Copyright information

© Hebrew University of Jerusalem 2018

Authors and Affiliations

  • Brooke Feigon
    • 1
  • Kimball Martin
    • 2
  • David Whitehouse
  1. 1.Department of MathematicsThe City College of New York, CUNYNew YorkUSA
  2. 2.Department of MathematicsUniversity of OklahomaNormanUSA

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