Dirichlet's theorem — may refer to any of several mathematical theorems due to Johann Peter Gustav Lejeune Dirichlet. Dirichlet s theorem on arithmetic progressions Dirichlet s approximation theorem Dirichlet s unit theorem Dirichlet conditions Dirichlet boundary… … Wikipedia
Dirichlet's theorem on arithmetic progressions — In number theory, Dirichlet s theorem, also called the Dirichlet prime number theorem, states that for any two positive coprime integers a and d, there are infinitely many primes of the form a + nd, where n ≥ 0. In other… … Wikipedia
Dirichlet's approximation theorem — In number theory, Dirichlet s theorem on Diophantine approximation, also called Dirichlet s approximation theorem, states that for any real number α and any positive integer N, there exists integers p and q such that 1 ≤ q ≤ N and This is a… … Wikipedia
Dirichlet conditions — Not to be confused with Dirichlet boundary condition. In mathematics, the Dirichlet conditions are sufficient conditions for a real valued, periodic function f(x) to be equal to the sum of its Fourier series at each point where f is continuous.… … Wikipedia
Dirichlet character — In number theory, Dirichlet characters are certain arithmetic functions which arise from completely multiplicative characters on the units of . Dirichlet characters are used to define Dirichlet L functions, which are meromorphic functions with a… … Wikipedia
Dirichlet density — This article is not about the Dirichlet distribution of probability theory. In mathematics, the Dirichlet density (or analytic density) of a set of primes, named after Johann Gustav Dirichlet, is a measure of the size of the set that is easier to … Wikipedia
Dirichlet eigenvalue — In mathematics, the Dirichlet eigenvalues are the fundamental modes of vibration of an idealized drum with a given shape. The problem of whether one can hear the shape of a drum is: given the Dirichlet eigenvalues, what features of the shape of… … Wikipedia
Dirichlet's unit theorem — In mathematics, Dirichlet s unit theorem is a basic result in algebraic number theory due to Gustav Lejeune Dirichlet.[1] It determines the rank of the group of units in the ring OK of algebraic integers of a number field K. The regulator is a… … Wikipedia
Dirichlet L-function — In mathematics, a Dirichlet L series is a function of the form Here χ is a Dirichlet character and s a complex variable with real part greater than 1. By analytic continuation, this function can be extended to a meromorphic function on the whole… … Wikipedia
Dirichlet distribution — Several images of the probability density of the Dirichlet distribution when K=3 for various parameter vectors α. Clockwise from top left: α=(6, 2, 2), (3, 7, 5), (6, 2, 6), (2, 3, 4). In probability and… … Wikipedia
