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A tensor notation which considers the Riemann tensor R_(lambdamunukappa) as a matrix R_((lambdamu)(nukappa)) with indices lambdamu and nukappa.

The image on the Riemann sphere of any circle under a complex rational mapping with numerator and denominator having degrees no more than n has length no longer than 2npi.

Asserts the existence and uniqueness of the extremal quasiconformal map between two compact Riemann surfaces of the same genus modulo an equivalence relation.

There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include 1. The ...

The Riemann sphere C^*=C union {infty}, also called the extended complex plane. The notation C^^ is sometimes also used (Krantz 1999, p. 82). The notation C^* is also used to ...

The complex plane C with the origin removed, i.e., C-{0}. The punctured plane is sometimes denoted C^* (although this notation conflicts with that for the Riemann sphere C-*, ...

A function that can be defined as a Dirichlet series, i.e., is computed as an infinite sum of powers, F(n)=sum_(k=1)^infty[f(k)]^n, where f(k) can be interpreted as the set ...

The Stieltjes integral is a generalization of the Riemann integral. Let f(x) and alpha(x) be real-valued bounded functions defined on a closed interval [a,b]. Take a ...

A pseudoanalytic function is a function defined using generalized Cauchy-Riemann equations. Pseudoanalytic functions come as close as possible to having complex derivatives ...

The Dirichlet lambda function lambda(x) is the Dirichlet L-series defined by lambda(x) = sum_(n=0)^(infty)1/((2n+1)^x) (1) = (1-2^(-x))zeta(x), (2) where zeta(x) is the ...