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Transactions of the American Mathematical Society

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



On existence of generic cusp forms on semisimple algebraic groups

Authors: Allen Moy and Goran Muić
Journal: Trans. Amer. Math. Soc. 370 (2018), 4731-4757
MSC (2010): Primary 11E70, 22E50
Published electronically: January 18, 2018
MathSciNet review: 3812094
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Abstract: In this paper we discuss the existence of certain classes of cuspidal automorphic representations having non-zero Fourier coefficients for a general semisimple algebraic group $ G$ defined over a number field $ k$ such that its Archimedean group $ G_\infty $ is not compact. When $ G$ is quasi-split over $ k$, we obtain a result on existence of generic cuspidal automorphic representations which generalize results of Vignéras, Henniart, and Shahidi. We also discuss: (i) the existence of cuspidal automorphic forms with non-zero Fourier coefficients for congruence of subgroups of $ G_\infty $, and (ii) applications related to the work of Bushnell and Henniart on generalized Whittaker models.

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Additional Information

Allen Moy
Affiliation: Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong

Goran Muić
Affiliation: Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia

Keywords: Cuspidal automorphic forms, Poincar\'e series, Fourier coefficients
Received by editor(s): September 17, 2015
Received by editor(s) in revised form: September 25, 2016
Published electronically: January 18, 2018
Additional Notes: The first author acknowledges Hong Kong Research Grants Council grant CERG #603813
The second author acknowledges Croatian Science Foundation grant no. 9364
Article copyright: © Copyright 2018 American Mathematical Society