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In his monumental treatise Disquisitiones Arithmeticae, Gauss conjectured that the class number h(-d) of an imaginary quadratic field with binary quadratic form discriminant ...

A module is a mathematical object in which things can be added together commutatively by multiplying coefficients and in which most of the rules of manipulating vectors hold. ...

There are nine possible types of isolated singularities on a cubic surface, eight of them rational double points. Each type of isolated singularity has an associated normal ...

Ramanujan's Dirichlet L-series is defined as f(s)=sum_(n=1)^infty(tau(n))/(n^s), (1) where tau(n) is the tau function. Note that the notation F(s) is sometimes used instead ...

For any ideal I in a Dedekind ring, there is an ideal I_i such that II_i=z, (1) where z is a principal ideal, (i.e., an ideal of rank 1). Moreover, for a Dedekind ring with a ...

Informally, an elliptic curve is a type of cubic curve whose solutions are confined to a region of space that is topologically equivalent to a torus. The Weierstrass elliptic ...

The companion matrix to a monic polynomial a(x)=a_0+a_1x+...+a_(n-1)x^(n-1)+x^n (1) is the n×n square matrix A=[0 0 ... 0 -a_0; 1 0 ... 0 -a_1; 0 1 ... 0 -a_2; | | ... ... |; ...

Eisenstein's irreducibility criterion is a sufficient condition assuring that an integer polynomial p(x) is irreducible in the polynomial ring Q[x]. The polynomial ...

Every polynomial equation having complex coefficients and degree >=1 has at least one complex root. This theorem was first proven by Gauss. It is equivalent to the statement ...

A separable extension K of a field F is one in which every element's algebraic number minimal polynomial does not have multiple roots. In other words, the minimal polynomial ...