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On periods of CUSP forms and algebraic cycles forU(3)

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Abstract

In this paper we discuss relations between the following types of conditions on a representationπ in a cuspidalL-packet ofU(3): (1)L(s, π×ξ) has a pole ats=1 for someξ; (2) aperiod ofπ over some algebraic cycle inU(3) (coming from a unitary group in two variables) is non-zero; and (3) π is atheta-series lifting from some unitary group in two variables. As an application of our analysis, we show that the algebraic cycles on theU(3) Shimura variety arenot spanned (over the Hecke algebra) by the modular and Shimura curves coming from unitary subgroups.

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Authors and Affiliations

  1. Department of Mathematics, The Weizmann Institute of Science, 76100, Rehovot, Israel

    S. Gelbart

  2. Department of Mathematics, UCLA, 90024, Los Angeles, California, USA

    J. Rogawski

  3. Department of Mathematics, Tel-Aviv University, 69978, Ramat Aviv, Israel

    D. Soudry

Authors
  1. S. Gelbart
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  2. J. Rogawski
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  3. D. Soudry
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Corresponding author

Correspondence to S. Gelbart.

Additional information

All three authors are supported by a grant from the U.S.-Israel Binational Science Foundation; the second author is also supported by an NSF Grant.

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Gelbart, S., Rogawski, J. & Soudry, D. On periods of CUSP forms and algebraic cycles forU(3). Israel J. Math. 83, 213–252 (1993). https://doi.org/10.1007/BF02764643

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  • DOI: https://doi.org/10.1007/BF02764643

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