eprintid: 10160063
rev_number: 7
eprint_status: archive
userid: 699
dir: disk0/10/16/00/63
datestamp: 2023-03-14 16:12:12
lastmod: 2023-03-14 16:12:12
status_changed: 2023-03-14 16:12:12
type: article
metadata_visibility: show
sword_depositor: 699
creators_name: Hill, R
title: Metaplectic covers of GLₙ and the Gauss-Schering lemma
ispublished: pub
divisions: UCL
divisions: B04
divisions: C06
divisions: F59
note: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
abstract: The Gauss-Schering Lemma is a classical formula for the Legendre symbol commonly used in elementary proofs of the quadratic reciprocity law. In this paper we show how the Gauss Schering Lemma may be generalized to give a formula for a 2-cocycle corresponding to a higher metaplectic extension of GLn/k for any global field k. In the case that k has positive characteristic, our formula gives a complete construction of the metaplectic group and consequently an independent proof of the power reciprocity law for k.
date: 2001
date_type: published
publisher: Cellule MathDoc/CEDRAM
official_url: https://doi.org/10.5802/jtnb.314
oa_status: green
full_text_type: pub
language: eng
primo: open
primo_central: open_green
verified: verified_manual
elements_id: 18310
doi: 10.5802/jtnb.314
lyricists_name: Hill, Richard
lyricists_id: RMHIL99
actors_name: Hill, Richard
actors_id: RMHIL99
actors_role: owner
full_text_status: public
publication: Journal de Théorie des Nombres de Bordeaux
volume: 13
number: 1
pagerange: 189-199
issn: 1246-7405
citation:        Hill, R;      (2001)    Metaplectic covers of GLₙ and the Gauss-Schering lemma.                   Journal de Théorie des Nombres de Bordeaux , 13  (1)   pp. 189-199.    10.5802/jtnb.314 <https://doi.org/10.5802/jtnb.314>.       Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/10160063/1/JTNB_2001__13_1_189_0.pdf