Exponential sums with polynomial values of the discrete logarithm

William D. Banks, Igor E. Shparlinski

Research output: Contribution to journalArticlepeer-review


We estimate exponential sums of the form [equation omitted for formatting reasons] where f is a polynomial with integer cofficients, and ind n is the discrete logarithm of n modulo an odd prime p and a primitive root g. We apply this estimate to show that the values ind n,..., (ind n)m, M + 1 ≤ n ≤ M + N, are uniformly and independently distributed modulo p - 1.
Original languageEnglish
Pages (from-to)67-72
Number of pages6
JournalUniform distribution theory
Issue number2
Publication statusPublished - 2007


  • discrete logarithm
  • primitive root
  • index
  • uniform distribution


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