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The circle method is a method employed by Hardy, Ramanujan, and Littlewood to solve many asymptotic problems in additive number theory, particularly in deriving an asymptotic ...

A set of orthogonal functions {phi_n(x)} is termed complete in the closed interval x in [a,b] if, for every piecewise continuous function f(x) in the interval, the minimum ...

Let E be a simply connected compact set in the complex plane. By the Riemann mapping theorem, there is a unique analytic function ...

The discrete uniform distribution is also known as the "equally likely outcomes" distribution. Letting a set S have N elements, each of them having the same probability, then ...

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, ...

A complex line bundle is a vector bundle pi:E->M whose fibers pi^(-1)(m) are a copy of C. pi is a holomorphic line bundle if it is a holomorphic map between complex manifolds ...

The inverse erf function is the inverse function erfc^(-1)(z) of erfc(x) such that erfc(erfc^(-1)(x))=erfc^(-1)(erfc(x)), (1) with the first identity holding for 0<x<2 and ...

Jonquière's relation, sometimes also spelled "Joncquière's relation" (Erdélyi et al. 1981, p. 31), states ...

The German mathematician Kronecker proved that all the Galois extensions of the rationals Q with Abelian Galois groups are subfields of cyclotomic fields Q(mu_n), where mu_n ...

The kei_nu(z) function is defined as the imaginary part of e^(-nupii/2)K_nu(ze^(pii/4))=ker_nu(z)+ikei_nu(z), (1) where K_nu(z) is a modified Bessel function of the second ...