ProofWiki:Mathematicians/Johann Lejeune Dirichlet

Full name: Johann Peter Gustav Lejeune Dirichlet.

German mathematician who worked mainly in the field of analysis.

Credited with the first formal definition of a function.

Married Rebecka Mendelssohn, the youngest sister of Fanny and Felix Mendelssohn.

Nationality

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

History

• Born: 13 Feb 1805, Düren, French Empire (now Germany)
• Died: 5 May 1859, Göttingen, Hanover (now Germany)

Theorems and Definitions

• Theorems named Dirichlet's Theorem:
  • Dirichlet's Approximation Theorem (Diophantine Analysis)
  • Dirichlet's Theorem on Arithmetic Progressions (Number Theory, specifically prime numbers)
  • Dirichlet's Unit Theorem (Algebraic Number Theory and Ring Theory)

• 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 Form
• Dirichlet Kernel (Functional Analysis, Fourier Series)
• Dirichlet Problem (Partial Differential Equations)
• Dirichlet Stability Criterion (Dynamical Systems)
• Dirichlet's Test for Uniform Convergence (Analysis)
• Dirichlet Boundary Condition (Differential Equations)
• Dirichlet Function (Topology)
• Pigeonhole Principle (also known as Dirichlet's Box (or Drawer) Principle (Combinatorics)
• Dirichlet Divisor Problem (currently unsolved) (Number Theory)
• Dirichlet Eta Function (Number Theory)
• Latent Dirichlet Allocation (Statistics)
• Class Number Formula (Analysis)
• Dirichlet Integral (Integral Calculus)
• Dirichlet Principle (Harmonic Functions) (Mathematical Physics)

Books and Papers

• 1863: Vorlesungen über Zahlentheorie

Also see

• John J. O'Connor and Edmund F. Robertson: "Johann Lejeune Dirichlet": MacTutor History of Mathematics archive

• George F. Simmons: Calculus Gems (1992): Chapter $\text {A}.28$