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Transactions of the American Mathematical Society

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The Spectral Kuznetsov Formula on $ SL(3)$


Author: Jack Buttcane
Journal: Trans. Amer. Math. Soc. 368 (2016), 6683-6714
MSC (2010): Primary 11F72; Secondary 44A20, 33E20
DOI: https://doi.org/10.1090/tran/6833
Published electronically: January 13, 2016
MathSciNet review: 3461048
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Abstract: The $ SL(3)$ Kuznetsov formula exists in several versions and has been employed with some success to study automorphic forms on $ SL(3)$. In each version, the weight functions on the geometric side are given by multiple integrals with complicated oscillating factors; this is the primary obstruction to its use. By describing them as solutions to systems of differential equations, we give power series and Mellin-Barnes integral representations of minimal dimension for these weight functions. This completes the role of harmonic analysis on symmetric spaces on the geometric side of the Kuznetsov formula, so that further study may be done through classical analytic techniques and should immediately open the door for results in the study of $ GL(3)$ $ L$-functions.


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Additional Information

Jack Buttcane
Affiliation: Mathematisches Institut, Georg-August Universität Göttingen, Bunsenstrasse 3-5, D-37073 Göttingen, Germany
Address at time of publication: Department of Mathematics, SUNY Buffalo, Buffalo, New York 14260
Email: buttcane@buffalo.edu

DOI: https://doi.org/10.1090/tran/6833
Received by editor(s): January 6, 2015
Published electronically: January 13, 2016
Additional Notes: During the time of this research, the author was supported by European Research Council Starting Grant agreement No. 258713.
Article copyright: © Copyright 2016 American Mathematical Society

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