Quadratic reciprocity and the sign of the Gauss sum via the finite Weil representation

Details Quadratic reciprocity and the sign of the Gauss sum via the finite Weil representation Quadratic reciprocity and the sign of the Gauss sum via the finite Weil representation

2008-08-18

arxiv.org/abs/0808.2447v3

Mathematics

Representation Theory

This paper was submited for publication February 1, 2008. Key words: Quadratic reciprocity, Sign of Gauss sum, Discrete Fourie

Scientific paper

We give new proofs of two basic results in number theory: The law of
quadratic reciprocity and the sign of the Gauss sum. We show that these results
are encoded in the relation between the discrete Fourier transform and the
action of the Weyl element in the Weil representation modulo p,q and pq.

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