Mathematician:Johann Peter Gustav Lejeune Dirichlet

Mathematician
German mathematician who worked mainly in the field of analysis.

Credited with the first formal definition of a function. Married, the youngest sister of and.

Nationality
German, although born in what was then part of the French empire.

History

 * Born: 13 Feb 1805, Düren, French Empire (now Germany)
 * 1855: Succeeded in professorship at Göttingen.
 * Died: 5 May 1859, Göttingen, Hanover (now Germany)

Definitions

 * Dirichlet Beta Function


 * Dirichlet Tessellation (also known as a Voronoi Diagram) and hence:
 * Dirichlet Cell
 * Dirichlet Polygon


 * Dirichlet Character in Number Theory, specifically:
 * Dirichlet Series (Analytic Number Theory)
 * Dirichlet L-function


 * Dirichlet Conditions (for Fourier Series)
 * Dirichlet Convolution (Number Theory and Arithmetic Functions)
 * Dirichlet Density (Number Theory)
 * Dirichlet Distribution (Probability Theory)
 * Generalized Dirichlet Distribution
 * Dirichlet Process
 * Dirichlet Eta Function (Number Theory)
 * Dirichlet Form
 * Dirichlet Function
 * Modified Dirichlet Function (also known as the Thomae Function or small Riemann function)
 * Dirichlet Kernel (Functional Analysis, Fourier Series)
 * Latent Dirichlet Allocation (Statistics)

Theorems

 * Theorems named Dirichlet's Theorem:
 * Dirichlet's Approximation Theorem (Diophantine Equations)
 * Dirichlet's Theorem on Arithmetic Sequences (Number Theory, specifically prime numbers)
 * Dirichlet's Unit Theorem (Algebraic Number Theory and Ring Theory)
 * Dirichlet's Theorem for 1-Dimensional Fourier Series, also known as Fourier's Theorem, for


 * Dirichlet Problem (Partial Differential Equations)
 * Dirichlet Stability Criterion (Dynamical Systems Theory)
 * Dirichlet's Test for Uniform Convergence (Analysis)
 * Dirichlet Boundary Condition (Differential Equations)


 * Dirichlet's Principle:
 * Dirichlet's Box (or Drawer) Principle (also known as the Pigeonhole Principle or Letterbox Principle) (Combinatorics)
 * Dirichlet's Principle (Harmonic Functions) (Mathematical Physics)


 * Dirichlet Divisor Problem (currently unsolved) (Number Theory)
 * Class Number Formula (Analysis)
 * Dirichlet Integral (Integral Calculus)

Publications

 * 1863:

Critical View

 * The story was told that young Dirichlet had as a constant companion on all his travels, like a devout man with his prayer book, an old, worn copy of the of .


 * Dirichlet was not satisfied to study 's Disquisitiones once or several times, but continued throughout his life to keep in close touch with the wealth of deep mathematical thoughts which it contains by perusing it again and again. For this reason the book was never put on the shelf but had an abiding place on the table at which he worked. Dirichlet was the first one who not only fully understood this work, but also made it accessible to others.

Also known as
Usually referred to as Peter Dirichlet.

The Johann is often ignored or forgotten even when specifying his name more fully: Peter Gustav Lejeune Dirichlet.