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2018 Higher weight on GL(3), II: The cusp forms
Jack Buttcane
Algebra Number Theory 12(10): 2237-2294 (2018). DOI: 10.2140/ant.2018.12.2237

Abstract

The purpose of this paper is to collect, extend, and make explicit the results of Gel’fand, Graev and Piatetski-Shapiro and Miyazaki for the GL(3) cusp forms which are nontrivial on SO(3,). We give new descriptions of the spaces of cusp forms of minimal K-type and from the Fourier–Whittaker expansions of such forms give a complete and completely explicit spectral expansion for L2(SL(3,)PSL(3,)), accounting for multiplicities, in the style of Duke, Friedlander and Iwaniec’s paper. We do this at a level of uniformity suitable for Poincaré series which are not necessarily K-finite. We directly compute the Jacquet integral for the Whittaker functions at the minimal K-type, improving Miyazaki’s computation. These results will form the basis of the nonspherical spectral Kuznetsov formulas and the arithmetic/geometric Kuznetsov formulas on GL(3). The primary tool will be the study of the differential operators coming from the Lie algebra on vector-valued cusp forms.

Citation

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Jack Buttcane. "Higher weight on GL(3), II: The cusp forms." Algebra Number Theory 12 (10) 2237 - 2294, 2018. https://doi.org/10.2140/ant.2018.12.2237

Information

Received: 9 April 2017; Revised: 15 April 2018; Accepted: 19 August 2018; Published: 2018
First available in Project Euclid: 14 February 2019

zbMATH: 07026818
MathSciNet: MR3911131
Digital Object Identifier: 10.2140/ant.2018.12.2237

Subjects:
Primary: 11F72
Secondary: 11F30

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.12 • No. 10 • 2018
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