2008/08/18 by Shamgar Gurevich, Ronny Hadani, Gurevich, Shamgar +3
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT
paper · pdf · doi:10.48550/arxiv.0808.2447
This paper was submited for publication February 1, 2008. Key words: Quadratic reciprocity, Sign of Gauss sum, Discrete Fourier transform, Finite Weil representations, Character of the Weil representation
arxiv created 2008/12/28 · arxiv updated 2009/12/01
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.