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In mathematics, there are several integrals known as the Dirichlet integral, after the German mathematician Peter Gustav Lejeune Dirichlet, one of which is the improper integral of the sinc function over the positive real number line.
The Vorlesungen contains two key results in number theory which were first proved by Dirichlet. The first of these is the class number formulae for binary quadratic forms. The second is a proof that arithmetic progressions contains an infinite number of primes (known as Dirichlet's theorem); this proof introduces Dirichlet L-series. These ...
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 is also a positive integer. In other words, there are infinitely many primes that are congruent to a modulo d.
Although the pigeonhole principle appears as early as 1624 in a book attributed to Jean Leurechon, [2] it is commonly called Dirichlet's box principle or Dirichlet's drawer principle after an 1834 treatment of the principle by Peter Gustav Lejeune Dirichlet under the name Schubfachprinzip ("drawer principle" or "shelf principle").
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Dirichlet's theorem may refer to any of several mathematical theorems due to Peter Gustav Lejeune Dirichlet. Dirichlet's theorem on arithmetic progressions; Dirichlet's approximation theorem; Dirichlet's unit theorem; Dirichlet conditions; Dirichlet boundary condition; Dirichlet's principle; Pigeonhole principle, sometimes also called Dirichlet ...
The question of finding solutions to such equations is known as the Dirichlet problem. In the sciences and engineering, a Dirichlet boundary condition may also be referred to as a fixed boundary condition or boundary condition of the first type. It is named after Peter Gustav Lejeune Dirichlet (1805–1859). [1]
Based on his research of the structure of the unit group of quadratic fields, he proved the Dirichlet unit theorem, a fundamental result in algebraic number theory. [15] He first used the pigeonhole principle, a basic counting argument, in the proof of a theorem in diophantine approximation, later named after him Dirichlet's approximation theorem.