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Conductors and newforms for U(1,1)

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Abstract

Let F be a non-Archimedean local field whose residue characteristic is odd. In this paper we develop a theory of newforms forU (1, 1)(F), building on previous work onSL 2(F). This theory is analogous to the results of Casselman forGL 2(F) and Jacquet, Piatetski-Shapiro, and Shalika forGL n(F). To a representation π ofU(1, 1)(F), we attach an integer c(π) called the conductor of π, which depends only on theL-packet π containing π. A newform is a vector in π which is essentially fixed by a congruence subgroup of level c(π). We show that our newforms are always test vectors for some standard Whittaker functionals, and, in doing so, we give various explicit formulae for newforms.

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Authors and Affiliations

  1. Department of Mathematics, American University, 20910, Washington DC, USA

    Joshua Lansky & A. Raghuram

  2. Department of Mathematics, University of Iowa, 14 Maclean Hall, 52242, Iowa City, IA, USA

    A. Raghuram

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  1. Joshua Lansky
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  2. A. Raghuram
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Correspondence to Joshua Lansky.

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Lansky, J., Raghuram, A. Conductors and newforms for U(1,1). Proc Math Sci 114, 319–343 (2004). https://doi.org/10.1007/BF02829439

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  • DOI: https://doi.org/10.1007/BF02829439

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