A splitting into the double cover of SL (3 , R)

Edmund Karasiewicz

doi:10.1007/s11139-021-00495-8

A splitting into the double cover of SL (3 , R)

Edmund Karasiewicz

Research output: Contribution to journal › Article › peer-review

Abstract

We provide a formula for the splitting of a congruence subgroup of SL(3 , R) into the double cover of SL(3 , R) in terms of Plücker coordinates. This new formula is then used to prove that the splitting satisfies a twisted multiplicativity. This formula has applications to the computation of Fourier coefficients of Eisenstein series on the double cover of SL(3) over Q.

Original language	English
Pages (from-to)	1489-1515
Number of pages	27
Journal	Ramanujan Journal
Volume	57
Issue number	4
DOIs	https://doi.org/10.1007/s11139-021-00495-8
State	Published - 1 Apr 2022
Externally published	Yes

Keywords

Eisenstein series
Metaplectic cover
Metaplectic forms

ASJC Scopus subject areas

Algebra and Number Theory

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10.1007/s11139-021-00495-8

Cite this

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abstract = "We provide a formula for the splitting of a congruence subgroup of SL(3 , R) into the double cover of SL(3 , R) in terms of Pl{\"u}cker coordinates. This new formula is then used to prove that the splitting satisfies a twisted multiplicativity. This formula has applications to the computation of Fourier coefficients of Eisenstein series on the double cover of SL(3) over Q.",

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author = "Edmund Karasiewicz",

note = "Funding Information: Acknowledgement The financial support by Swedish Energy Agency and Swedish Research Council is appreciated. Yuting Tan also appreciates scholarship from China Scholarship Council (CSC). Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

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N2 - We provide a formula for the splitting of a congruence subgroup of SL(3 , R) into the double cover of SL(3 , R) in terms of Plücker coordinates. This new formula is then used to prove that the splitting satisfies a twisted multiplicativity. This formula has applications to the computation of Fourier coefficients of Eisenstein series on the double cover of SL(3) over Q.

AB - We provide a formula for the splitting of a congruence subgroup of SL(3 , R) into the double cover of SL(3 , R) in terms of Plücker coordinates. This new formula is then used to prove that the splitting satisfies a twisted multiplicativity. This formula has applications to the computation of Fourier coefficients of Eisenstein series on the double cover of SL(3) over Q.

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KW - Metaplectic cover

KW - Metaplectic forms

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A splitting into the double cover of SL (3 , R)

Abstract

Keywords

ASJC Scopus subject areas

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