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The region 0<sigma<1, where sigma is defined as the real part of a complex number s=sigma+it. All nontrivial zeros (i.e., those not at negative even integers) of the Riemann ...

The boundary of complex hyperbolic 2-space.

The word modulus has several different meanings in mathematics with respect to complex numbers, congruences, elliptic integrals, quadratic invariants, sets, etc. The modulus ...

A polar representation of a complex measure mu is analogous to the polar representation of a complex number as z=re^(itheta), where r=|z|, dmu=e^(itheta)d|mu|. (1) The analog ...

A solution zeta_k=e^(2piik/d) to the cyclotomic equation x^d=1. The de Moivre numbers give the coordinates in the complex plane of the polygon vertices of a regular polygon ...

Let n be an integer such that n>=lambda_1, where lambda=(lambda_1,lambda_2,...) is a partition of n=|lambda| if lambda_1>=lambda_2>=...>=0, where lambda_i are a sequence of ...

A global field is either a number field, a function field on an algebraic curve, or an extension of transcendence degree one over a finite field. From a modern point of view, ...

Let A be a commutative complex Banach algebra. A nonzero homomorphism from A onto the field of complex numbers is called a character. Every character is automatically ...

A removable singularity is a singular point z_0 of a function f(z) for which it is possible to assign a complex number in such a way that f(z) becomes analytic. A more ...

An algorithm that can always be used to decide whether a given polynomial is free of zeros in the closed unit disk (or, using an entire linear transformation, to any other ...