Abstract
We revisit a classical result of Howe and Piatetski-Shapiro on the failure of strong multiplicity one for GSp(4).
Similar content being viewed by others
References
Casselman W.: On some results of Atkin and Lehner. Math. Ann. 201, 301–314 (1973)
Cogdell J.W., Piatetski-Shapiro I.I.: Base change for the Saito-Kurokawa representations of PGSp(4). J. Number Theory 30(3), 298– (1988)
Harris, M.: Non-vanishing of L-functions of 2 × 2 unitary groups. Forum Math. 5(4), 405–419 (1993)
Harris M., Kudla S.S.: Arithmetic automorphic forms for non-holomorphic discrete series of GSp(2). Duke Math. J. 66, 59–121 (1992)
Howe R., Piatetski-Shapiro I.I.: Some examples of automorphic forms on SP4. Duke Math. J. 50(1), 55–106 (1983)
Jacquet H., Shalika J.A.: On Euler products and the classification of automorphic representations I. Am. J. Math. 103(3), 499–558 (1981)
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)
Prasad, D.: Some remarks on representations of quaternion division algebras (preprint)
Prasad D., Schulze-Pillot R.: Generalised form of a conjecture of Jacquet and a local consequence. J. Reine Angew. Math. 616, 219–236 (2008)
Prasad D., Takloo-Bighash R.: Bessel models for GSp(4). J. Reine Angew. Math. 655, 189–243 (2011)
Roberts B.: The nonarchimedean theta correspondence for GSp(2) and GO(4). Trans. Am. Math. Soc. 351, 781–811 (1999)
Roberts B.: Global L-packets for GSp(2) and theta lifts. Doc. Math. 6, 247–314 (2001)
Saito H.: On Tunnell’s formula for characters of GL(2). Compos. Math. 85, 99–108 (1993)
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)
Takeda S.: Some local-global non-vanishing results of theta lifts for symplectic-orthogonal pairs. J. Reine Angew. Math. 657, 81–111 (2011)
Tunnell J.: Local \({\epsilon}\) -factors, and characters of GL(2). Am. J. Math. 105, 1277–1307 (1983)
Author information
Authors and Affiliations
Corresponding author
Additional information
To the memory of Ilya Piatetski-Shapiro.
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00229-012-0545-2