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Special representations of rank one orthogonal groups

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Abstract

We study the image of the theta correspondence from\(\overline {SL} (2)\) to a rank one orthogonal group (over a number field). The image consists of cusp forms, the Fourier coefficients of which satisfy a certain invariance property. We show that this property characterizes the image. The proof requires first an analogous local statement (almost everywhere) and then a use of certain Rankin-Selberg integrals.

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Authors and Affiliations

  1. School of Mathematical Sciences, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, 69978, Tel Aviv, Israel

    Ilya I. Piatetski-Shapiro & David Soudry

Authors
  1. Ilya I. Piatetski-Shapiro
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  2. David Soudry
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Partially supported by the Bat-Sheva de Rothschild Fund for the Advancement of Science and Technolog.

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Piatetski-Shapiro, I.I., Soudry, D. Special representations of rank one orthogonal groups. Israel J. Math. 64, 276–314 (1988). https://doi.org/10.1007/BF02882424

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  • DOI: https://doi.org/10.1007/BF02882424

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