In mathematics, the Dirac delta function, or function, is (informally) a generalized function on the real number line that is zero everywhere except at zero, with an integral of one over the entire real line. The delta function is sometimes thought of as an infinitely high, infinitely thin spike at the origin, with total area one under the spike, and physically represents an idealized point mass or point charge. It was introduced by theoretical physicist Paul Dirac. Dirac explicitly spoke of infinitely great values of his integrand. In the context of signal processing it is often ref...

In mathematics, a binary quadratic form is a quadratic form in two variables. More concretely, it is a homogeneous polynomial of degree 2 in two variables : q(x,y)=ax^2+bxy+cy^2, \, where a, b, c are the coefficients. Properties of binary quadratic forms depend in an essential way on the nature of the coefficients, which may be real numbers, rational numbers, or in the most delicate case, integers. Arithmetical aspects of the theory of binary quadratic forms are related to the arithmetic of quadratic fields and have been much studied, notably, by Gauss in Section V of Disquisitiones Ar...