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Let I(G) denote the set of all independent sets of vertices of a graph G, and let I(G,u) denote the independent sets of G that contain the vertex u. A fractional coloring of ...

The following are equivalent definitions for a Galois extension field (also simply known as a Galois extension) K of F. 1. K is the splitting field for a collection of ...

An isolated singularity is a singularity for which there exists a (small) real number epsilon such that there are no other singularities within a neighborhood of radius ...

The Kronecker-Weber theorem, sometimes known as the Kronecker-Weber-Hilbert theorem, is one of the earliest known results in class field theory. In layman's terms, the ...

An L-algebraic number is a number theta in (0,1) which satisfies sum_(k=0)^nc_kL(theta^k)=0, (1) where L(x) is the Rogers L-function and c_k are integers not all equal to 0 ...

A function is said to be modular (or "elliptic modular") if it satisfies: 1. f is meromorphic in the upper half-plane H, 2. f(Atau)=f(tau) for every matrix A in the modular ...

The field of all rational and irrational numbers is called the real numbers, or simply the "reals," and denoted R. The set of real numbers is also called the continuum, ...

If there exists a rational integer x such that, when n, p, and q are positive integers, x^n=q (mod p), then q is the n-adic residue of p, i.e., q is an n-adic residue of p ...

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 ...

Let x be a real number, and let R be the set of positive real numbers mu for which 0<|x-p/q|<1/(q^mu) (1) has (at most) finitely many solutions p/q for p and q integers. Then ...