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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 map is a way of associating unique objects to every element in a given set. So a map f:A|->B from A to B is a function f such that for every a in A, there is a unique ...

If a complex function f is analytic in a disk contained in a simply connected domain D and f can be analytically continued along every polygonal arc in D, then f can be ...

Let f:R->R, then the negative part of f is the function f^-:R->R defined by f^-(x)=max(-f(x),0). Note that the negative part is itself a nonnegative function. The negative ...

Given an amicable pair (m,n), the quantity sigma(m) = sigma(n) (1) = =s(m)+s(n) (2) = m+n (3) is called the pair sum, where sigma(n) is the divisor function and s(n) is the ...

The angular position of a quantity. For example, the phase of a function cos(omegat+phi_0) as a function of time is phi(t)=omegat+phi_0. The complex argument of a complex ...

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 ...

The term used in physics and engineering for a harmonic function. Potential functions are extremely useful, for example, in electromagnetism, where they reduce the study of a ...

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

Given a function f specified by parametric variables u_1, ..., u_n, a reparameterization f^^ of f over domain U is a change of variables u_i in U->v_i->V via a function phi ...