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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Supercuspidal representations and Poincaré series over function fields

Authors: Daniel Bump and Shuzo Takahashi
Journal: Trans. Amer. Math. Soc. 340 (1993), 395-413
MSC: Primary 11F12; Secondary 11R58
MathSciNet review: 1152320
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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.

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Article copyright: © Copyright 1993 American Mathematical Society