Journal article
Asymptotics for cuspidal representations by functoriality from GL(2)
Journal of number theory, Vol.164, pp.323-342
07/2016
DOI: 10.1016/j.jnt.2016.01.008
Abstract
Let π be a unitary automorphic cuspidal representation of GL2(QA) with Fourier coefficients λπ(n). Asymptotic expansions of certain sums of λπ(n) are proved using known functorial liftings from GL2, including symmetric powers, isobaric products, exterior squares, and base change. These asymptotic expansions are manifestation of the underlying functoriality and reflect value distribution of λπ(n) on integers, squares, cubes and fourth powers. •Asymptotics were proved for the following functorial liftings from GL(2):•The symmetric square, cube, and fourth power representations of π.•The isobaric product π1⊠π2 of unitary automorphic cuspidal representations π1 and π2 of GL2(QA).•The isobaric product π1⊠Sym2(π2).•The exterior square representation ∧2(π1⊠π2).•The base change from π to a Galois number field of prime degree over Q.
Details
- Title: Subtitle
- Asymptotics for cuspidal representations by functoriality from GL(2)
- Creators
- Huixue Lao - School of Mathematical Sciences, Shandong Normal University, Jinan, Shandong 250014, ChinaMark McKee - Department of Mathematics, The University of Iowa, Iowa City, IA 52242-1419, USAYangbo Ye - Department of Mathematics, The University of Iowa, Iowa City, IA 52242-1419, USA
- Resource Type
- Journal article
- Publication Details
- Journal of number theory, Vol.164, pp.323-342
- DOI
- 10.1016/j.jnt.2016.01.008
- ISSN
- 0022-314X
- eISSN
- 1096-1658
- Publisher
- Elsevier Inc
- Grant note
- DOI: 10.13039/100012906, name: Shandong Provincial Education Department
- Language
- English
- Date published
- 07/2016
- Academic Unit
- Mathematics
- Record Identifier
- 9983985984802771
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