Supercuspidal representations and Poincaré series over function fields
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- by Daniel Bump and Shuzo Takahashi PDF
- Trans. Amer. Math. Soc. 340 (1993), 395-413 Request permission
Abstract:
In this paper, we will give a new construction of certain cusp forms on $GL(2)$ over a rational function field. The forms which we construct are analogs of holomorphic modular forms, in that the local representations at the infinite place are in the discrete series. The novelty of our approach is that we are able to give a very explicit construction of these forms as certain ’Poincaré series.’ We will also study the exponential sums which arise in the Fourier expansions of these Poincaré series.References
- E.-U. Gekeler, Automorphe Formen über $\textbf {F}_q(T)$ mit kleinem Führer, Abh. Math. Sem. Univ. Hamburg 55 (1985), 111–146 (German). MR 831522, DOI 10.1007/BF02941492
- H. Jacquet and R. P. Langlands, Automorphic forms on $\textrm {GL}(2)$, Lecture Notes in Mathematics, Vol. 114, Springer-Verlag, Berlin-New York, 1970. MR 0401654, DOI 10.1007/BFb0058988 P. Kutzko, On the supercuspidal representations of $GL(2)$, I and II, Amer, J. Math. 100 (1978), 43-60 and 705-716.
- Ilya Piatetski-Shapiro, Complex representations of $\textrm {GL}(2,\,K)$ for finite fields $K$, Contemporary Mathematics, vol. 16, American Mathematical Society, Providence, R.I., 1983. MR 696772
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 340 (1993), 395-413
- MSC: Primary 11F12; Secondary 11R58
- DOI: https://doi.org/10.1090/S0002-9947-1993-1152320-4
- MathSciNet review: 1152320