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I'm new to this subject and wondering if anything is known specifically on the zero-th Gaussian periods of type (N,r), whereN is a product of distinct primesand r = p^s is a power of a prime. I know there are some very general results out there, but I haven't seen this so far. Thanks!

In case you don't know what I mean: Let X be the canonical additive character on GF(r) and let N be a divisor of r-1. Then the zero-th Gaussian period of type (N,r) is the sum of the values X(z) where z runs over all the elements of the (unique) multiplicative subgroup of GF(r) with order (r-1)/N.

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# Zero-th Gaussian periods

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