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Johann Peter Gustav Lejeune Dirichlet

 
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Johann Peter Gustav Lejeune Dirichlet
 
 
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Johann Peter Gustav Lejeune Dirichlet (; 13 February 1805 – 5 May 1859) was a German
Germany

Germany , officially the Federal Republic of Germany , is a country in Central Europe. It is bordered to the north by the North Sea, Denmark, and the Baltic Sea; to the east by Poland and the Czech Republic; to the south by Austria and Switzerland; and to the west by France, Luxembourg, Belgium, and the Netherlands....
 mathematician
Mathematician

A mathematician is a person whose primary area of study and/or research is the field of mathematics....
 credited with the modern "formal" definition of a function
Function (mathematics)

The mathematical concept of a function expresses dependence between two quantities, one of which is known and the other which is produced. A function associates a single output to each input element drawn from a fixed Set , such as the real numbers , although different inputs may have the same output....
.

His family hailed from the town of Richelette in Belgium
Belgium

* A small German-speaking Community of Belgium exists in eastern Wallonia. Belgium's linguistic diversity and related political and cultural conflicts are reflected in the history of Belgium and a complex Communities and regions of Belgium....
, from which his surname "Lejeune Dirichlet" ("", French
French language

French is a Romance language spoken around the world by around 80 million people as first language, by 190 million as second language, and by about another 200 million people as an acquired tongue, with significant speakers in 54 countries....
 for "the youth from Richelette") was derived. That was also where his grandfather lived.

Dirichlet was born in Düren
Düren

D?ren is a town in North Rhine-Westphalia, capital of D?ren . It is located between Aachen and Cologne on the river Rur....
, where his father was the postmaster
Postmaster

Postmaster refers to the head of an individual post office. When a postmaster is responsible for an entire mail distribution organization , the title of Postmaster General is commonly used....
.






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Johann Peter Gustav Lejeune Dirichlet (; 13 February 1805 – 5 May 1859) was a German
Germany

Germany , officially the Federal Republic of Germany , is a country in Central Europe. It is bordered to the north by the North Sea, Denmark, and the Baltic Sea; to the east by Poland and the Czech Republic; to the south by Austria and Switzerland; and to the west by France, Luxembourg, Belgium, and the Netherlands....
 mathematician
Mathematician

A mathematician is a person whose primary area of study and/or research is the field of mathematics....
 credited with the modern "formal" definition of a function
Function (mathematics)

The mathematical concept of a function expresses dependence between two quantities, one of which is known and the other which is produced. A function associates a single output to each input element drawn from a fixed Set , such as the real numbers , although different inputs may have the same output....
.

His family hailed from the town of Richelette in Belgium
Belgium

* A small German-speaking Community of Belgium exists in eastern Wallonia. Belgium's linguistic diversity and related political and cultural conflicts are reflected in the history of Belgium and a complex Communities and regions of Belgium....
, from which his surname "Lejeune Dirichlet" ("", French
French language

French is a Romance language spoken around the world by around 80 million people as first language, by 190 million as second language, and by about another 200 million people as an acquired tongue, with significant speakers in 54 countries....
 for "the youth from Richelette") was derived. That was also where his grandfather lived.

Dirichlet was born in Düren
Düren

D?ren is a town in North Rhine-Westphalia, capital of D?ren . It is located between Aachen and Cologne on the river Rur....
, where his father was the postmaster
Postmaster

Postmaster refers to the head of an individual post office. When a postmaster is responsible for an entire mail distribution organization , the title of Postmaster General is commonly used....
. He learned from Georg Ohm
Georg Ohm

Georg Simon Ohm was a German physicist. As a high school teacher, Ohm began his research with the recently invented electrochemical cell, invented by Italian Count Alessandro Volta....
 at the Jesuit gymnasium
Gymnasium (school)

A gymnasium is a type of school providing secondary education in some parts of Europe, comparable to English Grammar schools in the United Kingdoms or sixth form colleges and U.S....
 in Cologne
Cologne

Cologne is Germany's fourth-largest city , and is the largest city both in the German Federal State of North Rhine-Westphalia and within the Rhine-Ruhr, one of the major European metropolitan areas with more than ten million inhabitants....
. His first paper was on Fermat's last theorem
Fermat's Last Theorem

Fermat's Last Theorem is the name of the statement in number theory that states that:or, more precisely:In 1637 Pierre de Fermat wrote, in his copy of Claude Gaspard Bachet de M?ziriac's translation of the famous Arithmetica of Diophantus, "I have a truly marvellous proof of this proposition which this margin is too narrow to con...
 comprising a partial proof for the case , which was completed by Adrien-Marie Legendre
Adrien-Marie Legendre

Adrien-Marie Legendre was a France mathematician. He made important contributions to statistics, number theory, abstract algebra and mathematical analysis....
, who was one of the referees. Dirichlet completed his own proof almost at the same time; later he produced a full proof for the case .

He graduated from the University of Bonn
University of Bonn

The University of Bonn is a public research university located in Bonn, Germany. Founded in 1818 the University of Bonn is today one of the leading universities in Germany....
 in 1827 and taught as a Privatdozent
Privatdozent

Private docent is a title conferred in some European university systems, especially in German language-speaking countries, for someone who pursues an academic career and holds all formal qualifications to become a tenured university professor....
 at the University of Breslau, later teaching at the University of Berlin
Humboldt University of Berlin

The Humboldt University of Berlin is Berlin's oldest university, founded in 1810 as the University of Berlin by the liberal Prussian educational reformer and linguist Wilhelm von Humboldt, whose university model has strongly influenced other European and Western universities....
. In 1855 Dirichlet began teaching at the University of Göttingen.

In 1831, he married Rebecca Henriette Mendelssohn Bartholdy, who came from a distinguished family of converts from Judaism to Christianity; she was a granddaughter of the philosopher Moses Mendelssohn
Moses Mendelssohn

Moses Mendelssohn was a German Jewish philosopher to whose ideas the renaissance of European Jews, Haskalah is indebted. For some he was the third Moses heralding a new era in the history of the Jewish people....
, daughter of Abraham Mendelssohn Bartholdy
Abraham Mendelssohn Bartholdy

Abraham Mendelssohn Bartholdy was a German people Jewish banker and philanthropist. He was the father of Felix Mendelssohn and Fanny Mendelssohn....
 and a sister of the composers Felix Mendelssohn Bartholdy and Fanny Mendelssohn
Fanny Mendelssohn

Fanny C?cilie Mendelssohn , later Fanny Hensel, was a Germany pianist and composer, the sister of the composer Felix Mendelssohn and granddaughter of the philosopher Moses Mendelssohn....
.

Ferdinand Eisenstein
Ferdinand Eisenstein

Ferdinand Gotthold Max Eisenstein was a Germany mathematician. He specialized in number theory and mathematical analysis, and proved several results that eluded even Carl Friedrich Gauss....
, Leopold Kronecker
Leopold Kronecker

Leopold Kronecker was a Germany mathematician and logician who argued that arithmetic and Mathematical analysis must be founded on "whole numbers", saying, "God made the integers; all else is the work of man" ....
, and Rudolf Lipschitz
Rudolf Lipschitz

Rudolf Otto Sigismund Lipschitz was a Germany mathematician and professor at the University of Bonn from 1864. Peter Gustav Dirichlet was his teacher....
 were his students. After his death, Dirichlet's lectures and other results in number theory
Number theory

Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study....
 were collected, edited and published by his friend and fellow mathematician Richard Dedekind
Richard Dedekind

Julius Wilhelm Richard Dedekind was a Germany mathematics who did important work in abstract algebra, algebraic number theory and the foundations of the real numbers....
 under the title (Lectures on Number Theory).

See also

  • Theorems named Dirichlet's theorem:
    • Dirichlet's approximation theorem
      Dirichlet's approximation theorem

      In mathematics, Dirichlet's theorem on diophantine approximation, also called Dirichlet's approximation theorem, states that for any real number a, and any positive integer n, there is some positive integer m = n , such that the difference between ma and the nearest integer is at most ....
       (diophantine approximation
      Diophantine approximation

      In number theory, the field of Diophantine approximation, named after Diophantus of Alexandria, deals with the approximation of real numbers by rational numbers....
      )
    • Dirichlet's theorem on arithmetic progressions
      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 prime number of the form a + nd, where n = 0, or in other words: there are infinitely many primes which are congruence relation to a modular arithme...
       (number theory
      Number theory

      Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study....
      , specifically prime number
      Prime number

      In mathematics, a prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. An infinitude of prime numbers exists, as demonstrated by Euclid around 300 BC....
      s)
    • Dirichlet's theorem on diophantine approximation (number theory and approximation)
    • Dirichlet's unit theorem
      Dirichlet's unit theorem

      In algebraic number theory, Dirichlet's unit theorem determines the rank of an abelian group of the group of units in the ring OK of algebraic integers of a number field K....
       (algebraic number theory
      Algebraic number theory

      In mathematics, algebraic number theory is a major branch of number theory which studies the algebraic structures related to algebraic integers....
       and rings
      Ring (mathematics)

      In mathematics, a ring is a type of algebraic structure. There is some variation among mathematicians as to exactly what properties a ring is required to have, as described in detail below....
      )
  • Dirichlet beta function
    Dirichlet beta function

    In mathematics, the Dirichlet beta function is a special function, closely related to the Riemann zeta function. It is a particular Dirichlet L-function, the L-function for the alternating Dirichlet character of period four....
  • Dirichlet character
    Dirichlet character

    In number theory, Dirichlet characters are certain arithmetic functions which arise from completely multiplicative character theory on the units of ....
    s (number theory, specifically Zeta
    Dirichlet series

    In mathematics, a Dirichlet series is any series of the formwhere s and an, n = 1, 2, 3, ... are complex numbers....
     and L-functions
    Dirichlet L-function

    In mathematics, a Dirichlet L-series, named in honour of Johann Peter Gustav Lejeune Dirichlet, is a function of the formHere χ is a Dirichlet character and s a complex variable with real part greater than 1....
    . 1831)
  • Dirichlet conditions
    Dirichlet conditions

    In mathematics, the Dirichlet conditions are sufficient condition for a real numbers-valued, periodic function f to be equal the sum of its Fourier series at each point where f is continuous....
     (Fourier transform)
  • Dirichlet convolution
    Dirichlet convolution

    In mathematics, the Dirichlet convolution is a binary operation defined for arithmetic functions; it is of importance in number theory. This was developed by Johann Peter Gustav Lejeune Dirichlet, a German mathematician....
     (number theory and Arithmetic functions)
  • Dirichlet density
    Dirichlet density

    In mathematics, the Dirichlet density of a set of prime number, named after Dirichlet, is a measure of the size of the set that is easier to use than the natural density....
     (number theory)
  • Dirichlet distribution
    Dirichlet distribution

    In probability and statistics, the Dirichlet distribution , often denoted Dir, is a family of Continuous probability distribution multivariate random variable probability distributions parametrized by the vector α of positive real number....
     (probability theory)
  • Dirichlet form
  • Dirichlet kernel
    Dirichlet kernel

    In mathematical analysis, the Dirichlet kernel is the collection of functionsIt is named after Johann Peter Gustav Lejeune Dirichlet.The importance of the Dirichlet kernel comes from its relation to Fourier series....
     (functional analysis
    Functional analysis

    Functional analysis is the branch of mathematics, and specifically of mathematical analysis, concerned with the study of vector spaces and operators acting upon them....
    , Fourier series
    Fourier series

    In mathematics, a Fourier series decomposes a periodic function into a sum of simple oscillating functions, namely sine wave . The study of Fourier series is a branch of Fourier analysis....
    )
  • Dirichlet problem
    Dirichlet problem

    In mathematics, a Dirichlet problem is the problem of finding a function which solves a specified partial differential equation in the interior of a given region that takes prescribed values on the boundary of the region....
     (partial differential equation
    Partial differential equation

    In mathematics, partial differential equations are a type of differential equation, i.e., a Relation involving an unknown Function of several independent variables and its partial derivatives with respect to those variables....
    s)
  • Dirichlet series
    Dirichlet series

    In mathematics, a Dirichlet series is any series of the formwhere s and an, n = 1, 2, 3, ... are complex numbers....
     (analytic number theory
    Analytic number theory

    In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve number-theoretical problems....
    )
  • Dirichlet's test
    Dirichlet's test

    In mathematics, Dirichlet's test is a method of testing for the Convergent series of a series and is named after mathematician Johann Peter Gustav Lejeune Dirichlet....
     (analysis)
  • Dirichlet tessellation, also called a Voronoi diagram (geometry
    Geometry

    Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....
    )
  • Dirichlet boundary condition
    Dirichlet boundary condition

    In mathematics, the Dirichlet boundary condition is a type of boundary condition, named after Johann Peter Gustav Lejeune Dirichlet . When imposed on an ordinary differential equation or a partial differential equation, it specifies the values a solution needs to take on the boundary of the domain....
     (differential equation
    Differential equation

    A differential equation is a mathematics equation for an unknown function of one or several variable that relates the values of the function itself and its derivatives of various orders....
    s)
  • Dirichlet function (topology
    Topology

    Topology is a major area of mathematics that has emerged through the development of concepts from geometry and set theory, such as those of space, dimension, shape, transformation and others....
    )
  • Pigeonhole principle
    Pigeonhole principle

    In mathematics, the pigeonhole principle, also known as Dirichlet's box principle, is exemplified by such things as the fact that in a family of three children there must be at least two of the same gender....
    /Dirichlet's box (or drawer) principle (combinatorics
    Combinatorics

    Combinatorics is a branch of pure mathematics concerning the study of Countable set objects. It is related to many other areas of mathematics, such as algebra, probability theory, ergodic theory and geometry, as well as to applied subjects in computer science and statistical physics....
    )
  • Dirichlet divisor problem (currently unsolved) (Number theory)
  • Dirichlet eta function
    Dirichlet eta function

    In mathematics, in the area of analytic number theory, the Dirichlet eta function can be defined aswhere ζ is Bernhard Riemann Riemann zeta function....
     (number theory)
  • Latent Dirichlet allocation
    Latent Dirichlet allocation

    In statistics, latent Dirichlet allocation is a generative model that allows sets of observations to be explained by Latent variable groups which explain why some parts of the data are similar....
  • Class number formula
    Class number formula

    In number theory, the class number formula relates many important invariants of a number field to a special value of its Dedekind zeta function...
  • Dirichlet integral
    Dirichlet integral

    In mathematics, there are several integrals known as the Dirichlet integral, after the German mathematician Peter Gustav Lejeune Dirichlet....
  • Dirichlet principle
    Dirichlet principle

    In mathematics, Dirichlet's principle in potential theory states that, if the function u is the solution to Poisson's equationon a domain of a function of with boundary condition...
  • Generalized Dirichlet distribution
    Generalized Dirichlet distribution

    In statistics, the generalized Dirichlet distribution is a generalization of the Dirichlet distribution with a more general covariance structure and twice the number of parameters....
     (probability theory)
  • Dirichlet process
    Dirichlet process

    A Dirichlet process over , a set equipped with a suitable sigma-algebra, is a stochastic process whose sample path is a probability distribution on ....


External links

  • by Jürgen Elstrodt.
.
  • Dirichlet, Johann Peter Gustav Lejeune, , 1863. "".
  • found at .