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.
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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.
| Type: | Article |
|---|---|
| Title: | Metaplectic covers of GLₙ and the Gauss-Schering lemma |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.5802/jtnb.314 |
| Publisher version: | https://doi.org/10.5802/jtnb.314 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10160063 |
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