Gauss and Jacobi Sums
- 2.7k Downloads
In Chapter 6 we introduced the notion of a quadratic Gauss sum. In this chapter a more general notion of Gauss sum will be introduced. These sums have many applications. They will be used in Chapter 9 as a tool in the proofs of the laws of cubic and biquadratic reciprocity. Here we shall consider the problem of counting the number of solutions of equations with coefficients in a finite field. In this connection, the notion of a Jacobi sum arises in a natural way. Jacobi sums are interesting in their own right, and we shall develop some of their properties.
KeywordsFinite Field Unique Factorization Multiplicative Character Legendre Symbol Nonzero Complex Number
Unable to display preview. Download preview PDF.