The classical fact that every positive integer is a sum of four squares led to the much more general study of universal quadratic forms. Their behavior over extensions of the integers by elements such ...

Abstract: The maximization of a full-rank quadratic form over the binary alphabet can be performed through exponential-complexity exhaustive search. However, if the rank of the form is not a function ...

Let the random variable X = (X1, X2, ⋯, Xn) have the probability density $p(x) = \frac{\det^{\frac{1}{2}} \Omega}{(2\pi)^{n/2}} e^{-\frac{1}{2}x\Omega x'}$ where ...

We present a theory of classifying quadratic forms over an algebraic number field which is a reformulation of Eichler's methods and different from the traditional theory of Hasse. As applications we ...

The Doodle shows how the parabola changes with different numbers, making learning math fun and interactive for students.