On the algebraic structure of Gaussian periods

  title={On the algebraic structure of Gaussian periods},
  author={N. J. Wildberger},
Let p be a prime Zp the eld of residue classes mod p and Up the cyclic group of automorphisms of the additive group Zp We will identify Up with the non zero elements of Zp For any positive integer n dividing p there is exactly one subgroup C of Up of index n given by C fx j x Zp x g if jCj k then p kn The orbits of C on Zp are f g C together with the cosets of C in Up If y is a primitive root in Up then we may order the cosets C C C Cn so that yCi Ci for i n and yCn C In terms of y Ci fy n i j… CONTINUE READING