• Dirichlet algebra is a particular type of algebra associated to a compact Hausdorff space X. It is a closed subalgebra of C(X), the uniform algebra of...
    2 KB (323 words) - 07:41, 29 April 2025
  • Thumbnail for Peter Gustav Lejeune Dirichlet
    Johann Peter Gustav Lejeune Dirichlet (/ˌdɪərɪˈkleɪ/; German: [ləˈʒœn diʁiˈkleː]; 13 February 1805 – 5 May 1859) was a German mathematician. In number...
    31 KB (3,582 words) - 23:35, 29 June 2025
  • 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...
    24 KB (3,526 words) - 22:13, 17 June 2025
  • In mathematics, a Dirichlet series is any series of the form ∑ n = 1 ∞ a n n s , {\displaystyle \sum _{n=1}^{\infty }{\frac {a_{n}}{n^{s}}},} where s...
    25 KB (5,354 words) - 07:02, 13 May 2025
  • Thumbnail for Dirichlet convolution
    In mathematics, Dirichlet convolution (or divisor convolution) is a binary operation defined for arithmetic functions; it is important in number theory...
    16 KB (2,587 words) - 06:05, 30 April 2025
  • Thumbnail for Pigeonhole principle
    commonly called Dirichlet's box principle or Dirichlet's drawer principle after an 1834 treatment of the principle by Peter Gustav Lejeune Dirichlet under the...
    31 KB (4,190 words) - 00:29, 5 July 2025
  • and rings) Dirichlet algebra Dirichlet beta function Dirichlet boundary condition (differential equations) Neumann–Dirichlet method Dirichlet characters...
    3 KB (224 words) - 16:08, 20 March 2022
  • Thue–Siegel–Roth theorem says that, for algebraic irrational numbers, the exponent of 2 in the corollary to Dirichlet’s approximation theorem is the best we...
    9 KB (1,157 words) - 17:28, 12 July 2025
  • divisibility The convolution associated to the incidence algebra for intervals [1, n] becomes the Dirichlet convolution, hence the Möbius function is μ(a, b)...
    18 KB (3,019 words) - 12:52, 20 June 2025
  • In mathematics, the Dirichlet boundary condition is imposed on an ordinary or partial differential equation, such that the values that the solution takes...
    4 KB (435 words) - 14:50, 29 May 2024
  • Thumbnail for Abstract algebra
    In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations...
    33 KB (4,336 words) - 00:00, 30 June 2025
  • In mathematics, a Dirichlet problem asks for a function which solves a specified partial differential equation (PDE) in the interior of a given region...
    14 KB (2,013 words) - 13:00, 12 June 2025
  • In mathematics, Dirichlet's unit theorem is a basic result in algebraic number theory due to Peter Gustav Lejeune Dirichlet. It determines the rank of...
    13 KB (1,783 words) - 16:32, 28 June 2025
  • using the Risch algorithm. other nonelementary integrals, including the Dirichlet integral and elliptic integral. It follows directly from the definition...
    12 KB (1,291 words) - 01:37, 13 July 2025
  • In mathematics, the Hecke algebra is the algebra generated by Hecke operators, which are named after Erich Hecke. The algebra is a commutative ring. In...
    6 KB (576 words) - 02:55, 2 June 2025
  • the plane, and to finding analytic structure in the spectrum of a Dirichlet algebra." In 1996 he published an upper-level textbook Mathematical Analysis...
    6 KB (562 words) - 12:27, 27 May 2025
  • theory, the class number formula relates many important invariants of an algebraic number field to a special value of its Dedekind zeta function. We start...
    9 KB (1,302 words) - 16:23, 17 September 2024
  • Thumbnail for Algebraic number theory
    Lejeune Dirichlet's work was what led him to his later study of algebraic number fields and ideals. In 1863, he published Lejeune Dirichlet's lectures...
    40 KB (5,798 words) - 04:02, 10 July 2025
  • Generalized Riemann hypothesis (category Algebraic geometry)
    Dedekind zeta-functions), Maass forms, and Dirichlet characters (in which case they are called Dirichlet L-functions). When the Riemann hypothesis is...
    9 KB (1,330 words) - 18:07, 3 May 2025
  • \Longrightarrow \quad \mu (n)*\alpha ^{n}=n\,M(n)} by cancellation in the Dirichlet algebra. M ( 1 , n ) = 0  if  n > 1 M ( α , 1 ) = α M ( α , 2 ) = 1 2 ( α...
    8 KB (1,465 words) - 04:26, 19 April 2025
  • Dedekind, Riemann and Hilbert. Dirichlet does not explicitly recognise the concept of the group that is central to modern algebra, but many of his proofs show...
    8 KB (943 words) - 07:56, 18 February 2025
  • Biquadratic field Quadratic reciprocity Ideal class group Dirichlet's unit theorem Discriminant of an algebraic number field Ramification (mathematics) Root of...
    2 KB (187 words) - 23:15, 29 June 2024
  • In algebraic number theory, an algebraic integer is a complex number that is integral over the integers. That is, an algebraic integer is a complex root...
    12 KB (1,499 words) - 19:23, 5 June 2025
  • Thumbnail for Field (mathematics)
    Leo (2004), Modern algebra and the rise of mathematical structures (2nd ed.), Birkhäuser, ISBN 3-7643-7002-5, Zbl 1044.01008 Dirichlet, Peter Gustav Lejeune...
    86 KB (10,330 words) - 20:24, 2 July 2025
  • Thumbnail for Dirichlet eta function
    in the area of analytic number theory, the Dirichlet eta function is defined by the following Dirichlet series, which converges for any complex number...
    19 KB (3,708 words) - 17:02, 5 July 2025
  • f(n) = f(p)a f(q)b ... While the Dirichlet convolution of two multiplicative functions is multiplicative, the Dirichlet convolution of two completely multiplicative...
    6 KB (1,008 words) - 09:43, 9 August 2024
  • In mathematics, an algebra such as ( R , + , ⋅ ) {\displaystyle (\mathbb {R} ,+,\cdot )} has multiplication ⋅ {\displaystyle \cdot } whose associativity...
    25 KB (4,777 words) - 15:55, 29 May 2025
  • that the Dirichlet L {\displaystyle L} -function is nonzero at s = 1 {\displaystyle s=1} . Using much more advanced techniques including algebraic K-theory...
    52 KB (8,509 words) - 03:55, 10 July 2025
  • They occur, for example, in the functional equations of Dirichlet L-functions, where for a Dirichlet character χ the equation relating L(s, χ) and L(1 − s...
    7 KB (918 words) - 18:21, 8 June 2023
  • spectral set for T, and R ( X ) {\displaystyle {\mathcal {R}}(X)} is a Dirichlet algebra, then T has a minimal normal δX dilation, of the form above. A consequence...
    3 KB (533 words) - 13:48, 7 November 2023