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A remark on the failure of multiplicity one for GSp(4)

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Abstract

We revisit a classical result of Howe and Piatetski-Shapiro on the failure of strong multiplicity one for GSp(4).

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References

  1. Casselman W.: On some results of Atkin and Lehner. Math. Ann. 201, 301–314 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  2. Cogdell J.W., Piatetski-Shapiro I.I.: Base change for the Saito-Kurokawa representations of PGSp(4). J. Number Theory 30(3), 298– (1988)

    Article  MathSciNet  MATH  Google Scholar 

  3. Harris, M.: Non-vanishing of L-functions of 2 × 2 unitary groups. Forum Math. 5(4), 405–419 (1993)

    Google Scholar 

  4. Harris M., Kudla S.S.: Arithmetic automorphic forms for non-holomorphic discrete series of GSp(2). Duke Math. J. 66, 59–121 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  5. Howe R., Piatetski-Shapiro I.I.: Some examples of automorphic forms on SP4. Duke Math. J. 50(1), 55–106 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  6. Jacquet H., Shalika J.A.: On Euler products and the classification of automorphic representations I. Am. J. Math. 103(3), 499–558 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  7. Piatetski-Shapiro I.I.: Multiplicity one theorems. Automorphic forms representations and L-functions (Proceedings of Symposia in Pure Mathematics, Oregon State University, Corvallis, Ore., 1977), Part 1, pp. 209–212, Proceedings of Symposia in Pure Mathematics, XXXIII, American Mathematics Society, Providence, R.I., (1979)

  8. Prasad, D.: Some remarks on representations of quaternion division algebras (preprint)

  9. Prasad D., Schulze-Pillot R.: Generalised form of a conjecture of Jacquet and a local consequence. J. Reine Angew. Math. 616, 219–236 (2008)

    MathSciNet  MATH  Google Scholar 

  10. Prasad D., Takloo-Bighash R.: Bessel models for GSp(4). J. Reine Angew. Math. 655, 189–243 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  11. Roberts B.: The nonarchimedean theta correspondence for GSp(2) and GO(4). Trans. Am. Math. Soc. 351, 781–811 (1999)

    Article  MATH  Google Scholar 

  12. Roberts B.: Global L-packets for GSp(2) and theta lifts. Doc. Math. 6, 247–314 (2001)

    MathSciNet  MATH  Google Scholar 

  13. Saito H.: On Tunnell’s formula for characters of GL(2). Compos. Math. 85, 99–108 (1993)

    MATH  Google Scholar 

  14. Soudry D.: A uniqueness theorem for representations of GSO(6) and the strong multiplicity one theorem for generic representations of GSp(4). Israel J. Math. 58(3), 257–287 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  15. Takeda S.: Some local-global non-vanishing results of theta lifts for symplectic-orthogonal pairs. J. Reine Angew. Math. 657, 81–111 (2011)

    MathSciNet  MATH  Google Scholar 

  16. Tunnell J.: Local \({\epsilon}\) -factors, and characters of GL(2). Am. J. Math. 105, 1277–1307 (1983)

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Ramin Takloo-Bighash.

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To the memory of Ilya Piatetski-Shapiro.

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File, D., Takloo-Bighash, R. A remark on the failure of multiplicity one for GSp(4). manuscripta math. 140, 263–272 (2013). https://doi.org/10.1007/s00229-012-0545-2

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  • DOI: https://doi.org/10.1007/s00229-012-0545-2

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