The Spectral Kuznetsov Formula on $SL(3)$
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- by Jack Buttcane PDF
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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.References
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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
- MR Author ID: 884064
- Email: buttcane@buffalo.edu
- 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.
- © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 6683-6714
- MSC (2010): Primary 11F72; Secondary 44A20, 33E20
- DOI: https://doi.org/10.1090/tran/6833
- MathSciNet review: 3461048