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Transactions of the American Mathematical Society

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

 
 

 

On the size of $ p$-adic Whittaker functions


Author: Edgar Assing
Journal: Trans. Amer. Math. Soc. 372 (2019), 5287-5340
MSC (2010): Primary 11F70; Secondary 11L40, 11S80
DOI: https://doi.org/10.1090/tran/7685
Published electronically: December 7, 2018
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Abstract: In this paper we tackle a question raised by N. Templier and A. Saha concerning the size of Whittaker new vectors appearing in infinite-dimensional representations of $ {\rm GL}_2$ over nonarchimedean fields. We derive precise bounds for such functions in all possible situations. Our main tool is the $ p$-adic method of stationary phase.


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Additional Information

Edgar Assing
Affiliation: School of Mathematics, University of Bristol, Bristol, United Kingdom
Email: edgar.assing@bristol.ac.uk

DOI: https://doi.org/10.1090/tran/7685
Keywords: Automorphic representations, Whittaker new vectors, $p$-adic stationary phase, $p$-adic special functions
Received by editor(s): June 3, 2018
Received by editor(s) in revised form: August 14, 2018
Published electronically: December 7, 2018
Article copyright: © Copyright 2018 American Mathematical Society