Quadratic Gauss sum information

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...

Friedrich Gauss was the quadratic Gauss sum, for R the field of residues modulo a prime number p, and χ the Legendre symbol. In this case Gauss proved that...

incomplete sum is the partial sum of the quadratic Gauss sum (indeed, the case investigated by Gauss). Here there are good estimates for sums over shorter...

counting modulo a fixed prime. Eisenstein's proof of quadratic reciprocity is a simplification of Gauss's third proof. It is more geometrically intuitive and...

1808) (Determination of the sign of the quadratic Gauss sum, uses this to give the fourth proof of quadratic reciprocity) 1813: "Disquisitiones generales...

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...

theorems and formed conjectures about quadratic residues, but the first systematic treatment is § IV of Gauss's Disquisitiones Arithmeticae (1801). Article...

in order to produce various proofs of the quadratic reciprocity law. Gauss introduced the quadratic Gauss sum and used the formula ∑ k = 0 p − 1 ζ a k...

includes all of Gauss's papers on number theory: all the proofs of quadratic reciprocity, the determination of the sign of the Gauss sum, the investigations...

can be evaluated at z = −1 by using a quadratic transformation to change z = −1 to z = 1 and then using Gauss's theorem to evaluate the result. A typical...

Lagrange. In 1801 Gauss published Disquisitiones Arithmeticae, a major portion of which was devoted to a complete theory of binary quadratic forms over the...

Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks...

_{-1}^{1}f(x)\,dx\approx \sum _{i=1}^{n}w_{i}f(x_{i}),} which is exact for polynomials of degree 2n − 1 or less. This exact rule is known as the Gauss–Legendre quadrature...

methods, such as the Gauss–Seidel method. In LLSQ the solution is unique, but in NLLSQ there may be multiple minima in the sum of squares. Under the...

In mathematics, a binary quadratic form is a quadratic homogeneous polynomial in two variables q ( x , y ) = a x 2 + b x y + c y 2 , {\displaystyle q(x...

to Hardy.[clarification needed] It can be used to calculate the quadratic Gauss sum. The Poisson summation formula holds in Euclidean space of arbitrary...

}}={\sqrt {{\frac {1}{N-1.5}}\sum _{i=1}^{N}\left(x_{i}-{\bar {x}}\right)^{2}}},} The error in this approximation decays quadratically (as 1/N2), and it is suited...

polygons with n edges) are constructible and which are not? Carl Friedrich Gauss proved the constructibility of the regular 17-gon in 1796. Five years later...

In mathematics, Kummer sum is the name given to certain cubic Gauss sums for a prime modulus p, with p congruent to 1 modulo 3. They are named after Ernst...

elliptic Gauss sum is an analog of a Gauss sum depending on an elliptic curve with complex multiplication. The quadratic residue symbol in a Gauss sum is replaced...

F_{n,m}.} A quadratic form of a normal vector, i.e. a quadratic function q = ∑ x i 2 + ∑ x j + c {\textstyle q=\sum x_{i}^{2}+\sum x_{j}+c} of multiple...

theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial with...

form the simplest ring of quadratic integers. Gaussian integers are named after the German mathematician Carl Friedrich Gauss. The Gaussian integers are...

a, b and non-zero c. It is named after the mathematician Carl Friedrich Gauss. The graph of a Gaussian is a characteristic symmetric "bell curve" shape...

Gaussian binomial coefficients in his determination of the sign of the quadratic Gauss sum. Gaussian binomial coefficients occur in the counting of symmetric...