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The conjecture that the Artin L-function of any n-dimensional complex representation of the Galois group of a finite extension of the rational numbers Q is an Artin ...

A quantity which does not equal zero is said to be nonzero. A real nonzero number must be either positive or negative, and a complex nonzero number can have either real or ...

An upper semicontinuous function whose restrictions to all complex lines are subharmonic (where defined). These functions were introduced by P. Lelong and Oka in the early ...

That portion of mathematics dealing with functions of real variables. While this includes some portions of topology, it is most commonly used to distinguish that portion of ...

The generalized law of sines applies to a simplex in space of any dimension with constant Gaussian curvature. Let us work up to that. Initially in two-dimensional space, we ...

Two points z and z^S in C^* are symmetric with respect to a circle or straight line L if all circles and straight lines passing through z and z^S are orthogonal to L. Möbius ...

An isogonal mapping is a transformation w=f(z) that preserves the magnitudes of local angles, but not their orientation. A few examples are illustrated above. A conformal ...

Consider any star of n line segments through one point in space such that no three lines are coplanar. Then there exists a polyhedron, known as a zonohedron, whose faces ...

A path in the complex plane over which contour integration is performed to compute a contour integral. When choosing a contour to evaluate an integral on the real line, a ...

The Radon-Nikodym theorem asserts that any absolutely continuous complex measure lambda with respect to some positive measure mu (which could be Lebesgue measure or Haar ...