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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 ...

A symbol consisting of three rational numbers that can be used to describe uniform polyhedra based on how a point C in a spherical triangle can be selected so as to trace the ...

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 ...

A transcendental number is a (possibly complex) number that is not the root of any integer polynomial, meaning that it is not an algebraic number of any degree. Every real ...

Define the Airy zeta function for n=2, 3, ... by Z(n)=sum_(r)1/(r^n), (1) where the sum is over the real (negative) zeros r of the Airy function Ai(z). This has the ...

A branch point whose neighborhood of values wrap around the range a finite number of times p as their complex arguments theta varies from 0 to a multiple of 2pi is called an ...

The all-pairs shortest path problem is the determination of the shortest graph distances between every pair of vertices in a given graph. The problem can be solved using n ...

Let M^n be a compact n-dimensional oriented Riemannian manifold without boundary, let O be a group representation of pi_1(M) by orthogonal matrices, and let E(O) be the ...