Peter Gustav Lejeune Dirichlet

Johann Peter Gustav Lejeune Dirichlet ( [ ləʒœn diʀikle ː ] or [ ləʒœn diʀiʃle ː ]; born February 13, 1805 in Düren, † May 5, 1859 in Göttingen ) was a German mathematician.

Dirichlet taught in Berlin and Göttingen and worked mainly in the fields of analysis and number theory.

Life

Dirichlet's grandfather came from Verviers ( Belgium today, then Prince-Bishopric of Liège ) and moved to Düren, where he married a daughter of a family Düren. The father of the grandfather was the first to distinguish him from his father to the name Lejeune Dirichlet ( " the young Dirichlet " ), the name originated from Dirichlet de Richelette ("from Richelette " ) to a small Belgian town today.

With twelve years of Dirichlet first attended the now called Beethoven -Gymnasium Bonn. During this time he was supervised by Peter Joseph Elvenich, an acquaintance of the Dirichlet family. Two years later, he joined the Jesuit Gymnasium in Cologne, where he was instructed by Georg Simon Ohm. In May 1822 he began to study mathematics in Paris, where he met with the leading French mathematicians of this period - including Biot, Fourier, Francoeur, Hachette, Laplace, Lacroix, Legendre, and Poisson - together.

In 1825, he first drew attention to himself by proving along with Adrien -Marie Legendre for the special case n = 5, the Fermat's last theorem: For there is no non-trivial integer solution of the equation. Later, he gave another proof for the special case n = 14

In 1827 he received his doctorate from the University of Bonn honorary and habilitated in 1827 - on the recommendation of Alexander von Humboldt - a lecturer at the University of Breslau. 1828 pulled him Alexander von Humboldt in Berlin. Here he taught first at the general war school, and later he taught at the School of Architecture. In 1829 he became a Privatdozent in 1831 A.O. Professor and in 1839 full professor of mathematics at the University of Berlin.

Dirichlet married on May 22, 1832 Rebecca Henriette Mendelssohn, a sister of the composer Fanny Hensel and the Romantic composer Felix Mendelssohn. A great-grandson of Peter Gustav Lejeune Dirichlet was the philosopher Leonard Nelson.

In 1855, he joined in Göttingen as professor of higher mathematics in the footsteps of Carl Friedrich Gauss. He held until his death in 1859 this position.

Dirichlet conducted research mainly in the fields of partial differential equations, definite integral and number theory. He joined the previously separate areas of number theory and analysis. Dirichlet series are named as a generalization of the zeta function for him. He gave criteria for the convergence of Fourier series and proved the existence of infinitely many primes in arithmetic progressions, where the first term is relatively prime to the difference of successive elements. Named after him is the Dirichlet unit theorem on units in algebraic number fields. His new kind of considerations of potential theory were later used by Bernhard Riemann and developed. He was also involved in mathematical physics (including equilibrium shapes of rotating fluids). His lectures on number theory were published after his death by Richard Dedekind and provided with a famous separate annex.

His students included next to Dedekind and Bernhard Riemann, Gotthold Eisenstein, Rudolf Lipschitz and Hans Sommer.

In Dirichlet house in Göttingen, the violinist Joseph Joachim and Agathe von Siebold, the temporary fiancée of Brahms played music. There, visited him Karl August Varnhagen von Ense from Berlin and described in his diaries the house, the garden and the pavilion.

Dirichlet was buried in the St. Bartholomew Cemetery in Göttingen.

At the Weierstraße 17 in Düren, where Dirichlet's birth house stood, a memorial plaque to Dirichlet. The Dirichletweg in Düren is named after him.

Method, which go back to Dirichlet or named after him are

• Dirichlet's approximation theorem
• Dirichlet condition
• Dirichlet beta function
• Dirichlet function (or Dirichlet jump function )
• Dirichlet kernel
• Dirichlet's prime number theorem
• Dirichlet's Principle
• Dirichlet boundary condition
• Dirichlet series
• Dirichlet distribution
• Pigeonhole principle
• Dirichlet decomposition
• Convergence criterion of Dirichlet
• Dirichlet convolution (see Zahlentheoretische_Funktion # fold )

Works

• Sur la convergence of the séries trigonométriques qui servent à une fonction representer arbitraire the limites entre données, Journal of Pure and Applied Mathematics 4, 1829, pp. 157-169 (Google Books :; at arXiv :)
• Proof of the theorem that every infinite arithmetic progression whose first term and difference are integers with no common factor, contains infinitely many primes, Proceedings of the Royal Prussian Academy of Sciences in Berlin, 1837, pp. 45-71

Published posthumously

• Richard Dedekind (ed. ): Studies on a problem of hydrodynamics, Proceedings of the Royal Society of Sciences in Göttingen 8, 1860, pp. 3-42
• Richard Dedekind (eds.): Lectures on Number Theory, Friedrich Vieweg and Son, Braunschweig 1863 1871 1879 1894 (edited by Dirichlet's lectures from the winter 1856/57 and completed by Richard Dedekind, at Google Books: 1, 1st Edition, on the Internet Archive: 2nd, 2nd, 2nd, 2nd, 3rd, 3rd, 3rd, 3rd, 4th, 4th Edition; during GDZ: 2nd edition)
• F. Grube (ed.): Lectures on the acting in the inverse ratio of the square of the distance forces, BG Teubner, Leipzig 1876 1887 (after Dirichlet's lectures from the winter 1856/57, the Internet Archive: 1, 1st Edition, in Cornell University: 2nd edition)
• G. Lejeune Dirichlet 's works. In two volumes, Georg Reimer, Berlin Leopold Kronecker (ed.): Volume One, 1889 ( with portrait; the Internet Archive:, )
• Leopold Kronecker, Lazarus Fuchs ( ed.): Second Volume, 1897 (on the Internet Archive :)