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For questions about the algebraic concept of 'character': a function from a group into a field satisfying certain properties. Not to be confused with the more commonly known psychological term.

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Quadratic Gauss sums: Explicit determinations?

Can anyone please tell me (give me a reference, preferably) if there is any explicit determination of sums of the form $g(n,\chi):=\sum_{r=1}^{q}\chi(r)e(\frac{rn+r^2}{q})$ where $\chi$ is a Dirichlet …
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