Let $\chi$ be a Dirichlet character with modulus $q$. For $a \in \mathbb{Z}$, the **Gauss sum** associated to $\chi$ and $a$ is given by
$$
\large \tau_{a}(\chi) = \sum_{r \,\in\, \mathbb{Z}/q\mathbb{Z}} \chi(r)\, e^{2\pi iar/q}.
$$
The Gauss sum $\tau_1(\chi)$ is often called "the Gauss sum" of $\chi$.

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- Last edited by Alina Bucur on 2018-07-04 18:11:09

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- 2018-07-04 18:11:09 by Alina Bucur (Reviewed)