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On the cubic Shimura lift for PGL3

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Abstract

Two types of evidence are presented for the conjecture that the image of the cubic Shimura correspondence for PGL3 is characterized by the nonvanishing of a certain period. Specifically, if a cusp from occurs in the pullback of the automorphic theta function on SO8 under the adjoint homomorphism PGL3 → SO8, then the cusp form is conjectured to be a Shimura lift.

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Authors and Affiliations

  1. Department of Mathematics, Stanford University, 94305-2125, Stanford, CA, USA

    Daniel Bump

  2. Department of Mathematics, Boston College, 02467-3806, Chestnut Hill, MA, USA

    Solomon Friedberg

  3. School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Ramat-Aviv, Israel

    David Ginzburg

Authors
  1. Daniel Bump
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  2. Solomon Friedberg
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  3. David Ginzburg
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Bump, D., Friedberg, S. & Ginzburg, D. On the cubic Shimura lift for PGL3 . Isr. J. Math. 126, 289–307 (2001). https://doi.org/10.1007/BF02784158

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  • DOI: https://doi.org/10.1007/BF02784158

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