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The Bunyakovsky conjecture generalizes Dirichlet's theorem to higher-degree polynomials. Whether or not even simple quadratic polynomials such as x 2 + 1 (known from Landau's fourth problem) attain infinitely many prime values is an important open problem. Dickson's conjecture generalizes Dirichlet's theorem to more than one polynomial.
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 mathematics, Dirichlet's unit theorem is a basic result in algebraic number theory due to Peter Gustav Lejeune Dirichlet. [1] It determines the rank of the group of units in the ring O K of algebraic integers of a number field K. The regulator is a positive real number that determines how "dense" the units are.
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 ...
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.
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