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