An elementary proof of the law of quadratic reciprocity over function fields

作者：Ji Chun Gang^*; Xue Yan

来源：Proceedings of the American Mathematical Society, 2008, 136(9): 3035-3039.

DOI：10.1090/S0002-9939-08-09327-1

• rational function fields
• Legendre symbol
• quadratic reciprocity law

Let P and Q be relatively prime monic irreducible polynomials in F-q[T] (2 inverted iota q). In this paper, we give an elementary proof for the following law of quadratic reciprocity in F-q[T]: (Q/P) (P/Q) = (-1) vertical bar P vertical bar-1/2 vertical bar Q vertical bar-1/2, where (Q/P) is the Legendre symbol.

• 单位
  南京师范大学