Riemann zeta function

短语

黎曼ζ函数

词形变化

Riemann zeta functions 复数 Riemann zeta functions

别名

Riemann zeta-function Riemann's zeta function

释义与例句

n.
  1. 1.

    The function ζ defined by the Dirichlet series ζ(s)=∑ₙ₌₁ ᪲1/(nˢ)=1/(1ˢ)+1/(2ˢ)+1/(3ˢ)+1/(4ˢ)+⋯, which is summable for points s in the complex half-plane with real part > 1; the analytic continuation of said function, being a holomorphic function defined on the complex numbers with pole at 1.

    黎曼ζ函数

    不可数 数学

    2009, Arthur T. Benjamin, Ezra Brown (editors), Biscuits of Number Theory, Mathematical Association of America, page 195, The Riemann zeta function is the function ζ(s)=∑ₙ₌₁ ᪲n⁻ˢ for s a complex number whose real part is greater than 1. […] The historical moments include Euler's proof that there are infinitely many primes, in which he proves ζ(s)=∏ₚₚᵣᵢₘₑ(1-1/(pˢ))⁻¹ as well as Riemann's statement of his hypothesis and several others. Beineke and Hughes then define the moment of the modulus of the Riemann zeta function by I_k(T)=1/T∫₀ ᪲|ζ(1/2+it)|²ᵏdt and take us through the work of several mathematicians on properties of the second and fourth moments.

  2. 2.

    A usage of (a specified value of) the Riemann zeta function, such as in an equation.

    可数 不可数

    2005, Jay Jorgenson, Serge Lang, Posₙ(R) and Eisenstein Series, Springer, Lecture Notes in Mathematics 1868, page 134, When the eigenfunctions are characters, these eigenvalues are respectively polynomials, products of ordinary gamma functions, and products of Riemann zeta functions, with the appropriate complex variables.

词源

Named after German mathematician Bernhard Riemann.

来源：wiktionary