Explore: Gauss Sums

non-unit r, where it takes the value 0. Gauss sums are the analogues for finite fields of the Gamma function. Such sums are ubiquitous in number theory. They

In number theory, quadratic Gauss sums are certain finite sums of roots of unity. A quadratic Gauss sum can be interpreted as a linear combination of

Johann Carl Friedrich Gauss (/ɡaʊs/ ; German: Gauß [kaʁl ˈfʁiːdʁɪç ˈɡaʊs] ; Latin: Carolus Fridericus Gauss; 30 April 1777 – 23 February 1855) was a German

restricted by some inequality. Examples of complete exponential sums are Gauss sums and Kloosterman sums; these are in some sense finite field or finite ring analogues

exponential sum over Dirichlet characters Elliptic Gauss sum, an analog of a Gauss sum Quadratic Gauss sum Gaussian quadrature Gauss–Hermite quadrature Gauss–Jacobi

of sums of roots of unity, now generally called Gauss sums (sometimes Gaussian sums). The quantity P − P* presented above is a quadratic Gauss sum mod

the higher Gauss sums: ζ n = ∑ a d a 2 θ a n | ∑ a d a 2 θ a n | . {\displaystyle \zeta _{n}={\frac {\sum _{a}d_{a}^{2}\theta _{a}^{n}}{|{\sum _{a}d_{a}^{2}\theta

primitive pth root of unity. This is a quadratic Gauss sum. A fundamental property of these Gauss sums is that g p 2 = p ∗ {\displaystyle g_{p}^{2}=p^{*}}

discrete logarithm problem reduces to Gauss sum estimation, an efficient classical algorithm for estimating Gauss sums would imply an efficient classical

The Gauss–Newton algorithm is used to solve non-linear least squares problems, which is equivalent to minimizing a sum of squared function values. It is