Have number theoretic functions such as Gauss sums been studied from a complexity view point? Where can I get a good introduction into complexity of Gauss sum estimation (beyond the quadratic case)?
Actually I was looking for something more than the answers given. It is known Gauss sums have a random walk behavior than is exploited in designing low-correlation sequences. Also Montogomery's conjecture provides a tighter bound than the Weil bounds of Deligne under the assumption of random behavior (deeper exposition in the book by Katz and Sarnak - the material of which I am not familiar). I was actually curious whether such randomness has been utilized in computer science. It seems very possible there are uses.