Peter Dirichlet

Johann Peter Gustav Lejeune Dirichlet
Born	February 13, 1805 Düren, French Empire
Died	May 5, 1859 Göttingen, Hanover
Residence	Germany
Nationality	German
Field	Mathematician
Institution	University of Berlin
Alma mater	University of Bonn
Academic advisor	Simeon Poisson Joseph Fourier
Notable students	Ferdinand Eisenstein Leopold Kronecker Carl Wilhelm Borchardt
Known for	Dirichlet function Dirichlet eta function

Johann Peter Gustav Lejeune Dirichlet [ləˈʒœn diʀiˈkle] (February 13, 1805 – May 5, 1859) was a German mathematician credited with the modern "formal" definition of a function. Image File history File links Please see the file description page for further information. ... February 13 is the 44th day of the year in the Gregorian calendar. ... 1805 was a common year starting on Tuesday (see link for calendar). ... Düren is a town in North Rhine-Westphalia, capital of Düren district. ... The term French Empire can refer to: The First French Empire of Napoleon Bonaparte (1804 - 1814 or 1815) The Second French Empire of Napoleon III (1852 - 1870) The Second French Colonial Empire (1830 - 1960) This is a disambiguation page — a navigational aid which lists other pages that might otherwise... May 5 is the 125th day of the year in the Gregorian Calendar (126th in leap years). ... 1859 (MDCCCLIX) is a common year starting on Saturday of the Gregorian calendar (or a common year starting on Monday of the Julian calendar). ... Göttingen ( ) is a city in Lower Saxony, Germany. ... Hanover (German: Hannover ( ) []), on the river Leine, is the capital of the federal state of Lower Saxony (Niedersachsen), Germany. ... Image File history File links Flag_of_Germany. ... Image File history File links Flag_of_Germany. ... Leonhard Euler is considered by many to be one of the greatest mathematicians of all time A mathematician is the person whose primary area of study and research is the field of mathematics. ... There is no institution called the University of Berlin, but there are four universities in Berlin, Germany: Humboldt University of Berlin (Humboldt-Universität zu Berlin) Technical University of Berlin (Technische Universität Berlin) Free University of Berlin (Freie Universität Berlin) Berlin University of the Arts (Universität der... The main building, viewed from the Hofgarten. ... Simeon Poisson. ... Jean Baptiste Joseph Fourier (March 21, 1768 - May 16, 1830) was a French mathematician and physicist who is best known for initiating the investigation of Fourier series and their application to problems of heat flow. ... Ferdinand Gotthold Max Eisenstein (April 16, 1823 - October 11, 1852) was a German mathematician. ... Leopold Kronecker Leopold Kronecker (December 7, 1823 - December 29, 1891) was a German mathematician and logician who argued that arithmetic and analysis must be founded on whole numbers, saying, God made the integers; all else is the work of man (Bell 1986, p. ... Carl Wilhelm Borchardt (22 February 1817 _ 27 June 1880) was a German mathamatition. ... In mathematics, a nowhere continuous function, also called an everywhere discontinuous function, is a function that is not continuous at any point of its domain. ... The Dirichlet eta function can be defined as where ζ is Riemanns zeta function. ... February 13 is the 44th day of the year in the Gregorian calendar. ... 1805 was a common year starting on Tuesday (see link for calendar). ... May 5 is the 125th day of the year in the Gregorian Calendar (126th in leap years). ... 1859 (MDCCCLIX) is a common year starting on Saturday of the Gregorian calendar (or a common year starting on Monday of the Julian calendar). ... Leonhard Euler is considered by many to be one of the greatest mathematicians of all time A mathematician is the person whose primary area of study and research is the field of mathematics. ... Partial plot of a function f. ...

His family hailed from the town of Richelet in Belgium, from which his surname "Lejeune Dirichlet" ("le jeune de Richelet", French for "the young chap from Richelet") was derived, and that was where his grandfather lived.

Dirichlet was born in Düren, where his father was the postmaster. He was educated in Germany, and then France, where he learnt from many of the most renowned mathematicians of the day. He also learned from Georg Ohm. His first paper was on Fermat's last theorem comprised of a partial proof for the case n = 5, which was completed by Adrien-Marie Legendre, who was one of the referees. Dirichlet also completed his own proof almost at the same time; he later also produced a full proof for the case n = 14. Düren is a town in North Rhine-Westphalia, capital of Düren district. ... If you are looking for different meanings of this word, see Postmaster (disambiguation) A postmaster is a term used in post offices to denote the head or master of the office. ... Georg Simon Ohm, (March 16, 1789 Erlangen, Germany - July 6, 1854, Munich) a German physicist, was born in Erlangen and educated at the university there. ... Pierre de Fermat Problem II.8 in the Arithmetica of Diophantus, annotated with Fermats comment which became Fermats Last Theorem (edition of 1670). ... Adrien-Marie Legendre (September 18, 1752 – January 10, 1833) was a French mathematician. ...

He married Rebecka Mendelssohn Bartholdy, who came from a distinguished family of converts from Judaism to Christianity; she was a granddaughter of the philosopher Moses Mendelssohn, daughter of Abraham Mendelssohn Bartholdy and a sister of the composer Felix Mendelssohn Bartholdy. Moses Mendelssohn Moses Mendelssohn (September 6, 1729 – January 4, 1786) was a German Jewish philosopher. ... Abraham Mendelssohn Bartholdy was a German Jewish banker and philanthropist, born Abraham Mendelssohn 10th December 1776 in Berlin, died there 19th December 1835. ... Felix Mendelssohn wrote his first symphony at the young age of fifteen. ...

Ferdinand Eisenstein, Leopold Kronecker, and Rudolf Lipschitz were his students. After his death, Dirichlet's lectures and other results in number theory were collected, edited and published by his friend and fellow mathematician Richard Dedekind under the title Vorlesungen über Zahlentheorie (Lectures on Number Theory). Ferdinand Gotthold Max Eisenstein (April 16, 1823 - October 11, 1852) was a German mathematician. ... Leopold Kronecker Leopold Kronecker (December 7, 1823 - December 29, 1891) was a German mathematician and logician who argued that arithmetic and analysis must be founded on whole numbers, saying, God made the integers; all else is the work of man (Bell 1986, p. ... Rudolf Otto Sigismund Lipschitz (May 14, 1832 – October 7, 1903) was a German mathematician and Professor at the University of Bonn from 1864. ... 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. ... Richard Dedekind Julius Wilhelm Richard Dedekind (October 6, 1831 – February 12, 1916) was a German mathematician who did important work in abstract algebra and the foundations of the real numbers. ... Vorlesungen über Zahlentheorie (Lectures on Number Theory) is a textbook of number theory written by German mathematicians P.G.L. Dirichlet and Richard Dedekind, and published in 1863. ...

See also

• Theorems named Dirichlet's theorem:
  • Dirichlet's theorem on arithmetic progressions (number theory, specifcally prime numbers)
  • Dirichlet's theorem on diophantine approximation (number theory and aproximation)
  • Dirichlet's unit theorem (algebraic number theory and rings)
• Dirichlet characters (number theory, specifically Zeta and L-functions. 1831)
• Dirichlet conditions (Fourier transform)
• Dirichlet convolution (number theory and Arithmetic functions)
• Dirichlet density (number theory)
• Dirichlet distribution (probability theory)
• Dirichlet kernel (functional analysis, Fourier series)
• Dirichlet problem (partial differential equations)
• Dirichlet series (analytic number theory)
• Dirichlet tessellation, also called a Voronoi diagram (geometry)
• Dirichlet boundary condition (differential equations)
• Dirichlet function (topology)
• Pigeonhole principle (combinatorics)
• Dirichlet divisor problem (currently unsolved) (Number theory)
• Dirichlet eta function (Number theory)
• Latent Dirichlet Allocation

In number theory, Dirichlets 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, or in other words: there are infinitely many primes which are congruent to a modulo d. ... 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. ... In mathematics, Dirichlets theorem on diophantine approximation, also called Dirichlets approximation theorem, states that for any real number α, and any positive integer n, there is some positive integer m ≤ n , such that the difference between mα and the nearest integer is at most 1/(n + 1). ... In algebraic number theory, Dirichlets unit theorem determines the rank of the group of units in the ring OK of algebraic integers of a number field K. The statement is that the rank is r + s − 1 where r is the number of real embeddings and 2s the number... This article or section does not cite its references or sources. ... Look up ring in Wiktionary, the free dictionary. ... In number theory, a Dirichlet character is a function χ from the positive integers to the complex numbers which has the following properties: There exists a positive integer k such that χ(n) = χ(n + k) for all n. ... Leopold I 1831 (MDCCCXXXI) was a common year starting on Saturday (see link for calendar). ... In mathematics, the Dirichlet conditions are sufficient condition for a periodic function f(x), to have a Fourier series representation or to possess a Fourier Transform. ... In mathematics, the Dirichlet convolution is a binary operation defined for arithmetic functions; it is of importance in number theory. ... In number theory, an arithmetic function (or number-theoretic function) f(n) is a function defined for all positive integers and having values in the complex numbers. ... In mathematics, the Dirichlet density (or analytic density) of a set of primes, named after Dirichlet, is a measure of the size of the set that is easier to use than the natural density. ... In probability and statistics, the Dirichlet distribution (after Johann Peter Gustav Lejeune Dirichlet) is a continuous multivariate probability distribution. ... In mathematical analysis, the Dirichlet kernel is the collection of functions It is named after Johann Peter Gustav Lejeune Dirichlet. ... Functional analysis is the branch of mathematics, and specifically of analysis, concerned with the study of spaces of functions. ... The Fourier series is a mathematical tool used for analyzing an arbitrary periodic function by decomposing it into a weighted sum of much simpler sinusoidal component functions sometimes referred to as normal Fourier modes, or simply modes for short. ... In mathematics, Dirichlet problems are a class of partial differential equation (PDE) problems which ask you to solve for the values of a function in a region given the value of the function on the boundary of that region. ... In mathematics, a partial differential equation (PDE) is a relation involving an unknown function of several independent variables and its partial derivatives with respect to those variables. ... In mathematics, a Dirichlet series, one of a number of concepts named in honor of Johann Peter Gustav Lejeune Dirichlet, is a series of the form The most famous of Dirichlet series is which is the Riemann zeta function. ... Analytic number theory is the branch of number theory that uses methods from mathematical analysis. ... This is the Voronoi diagram of a random set of points in the plane (all points lie within the image). ... Table of Geometry, from the 1728 Cyclopaedia. ... In mathematics, a Dirichlet boundary condition imposed on an ordinary differential equation or a partial differential equation specifies the values a solution is to take on the boundary of the domain. ... An illustration of a differential equation. ... In mathematics, a nowhere continuous function, also called an everywhere discontinuous function, is a function that is not continuous at any point of its domain. ... A Möbius strip, a surface with only one side and one edge; such shapes are an object of study in topology. ... The inspiration for the name of the principle: pigeons in holes. ... Combinatorics is a branch of mathematics that studies collections (usually finite) of objects that satisfy specified criteria. ... The summatory function, with leading terms removed, for The summatory function, with leading terms removed, for The summatory function, with leading terms removed, for , graphed as a distribution or histogram. ... The Dirichlet eta function can be defined as where ζ is Riemanns zeta function. ... A means of determining the topic of text automatically using variational methods and graphical models developed by Dave Blei and Michael Jordan. ...

External links

• Johann Peter Gustav Lejeune Dirichlet at the Mathematics Genealogy Project
• O'Connor, John J., and Edmund F. Robertson. "Johann Peter Gustav Lejeune Dirichlet". MacTutor History of Mathematics archive.
• Dirichlet, Johann Peter Gustav Lejeune, Vorlesungen über Zahlentheorie. Braunschweig, 1863. "Number Theory for the Millennium".
• Biography of Dirichlet found at Fermat's Last Theorem Blog