Gauss and Jacobi Sums

  • Kenneth Ireland
  • Michael Rosen
Part of the Graduate Texts in Mathematics book series (GTM, volume 84)


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.


Finite Field Unique Factorization Multiplicative Character Legendre Symbol Nonzero Complex Number 
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Copyright information

© Springer Science+Business Media New York 1982

Authors and Affiliations

  • Kenneth Ireland
    • 1
  • Michael Rosen
    • 2
  1. 1.Department of MathematicsUniversity of New BrunswickFrederictonCanada
  2. 2.Department of MathematicsBrown UniversityProvidenceUSA

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