Riemann zeta function

名词 n.
中文释义

英文释义

名词 n.
  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. uncountable,usually
    — It is straightforward to show that the Riemann zeta function has zeros at the negative even integers and these are called the trivial zeros of the Riemann zeta function.
  2. A usage of (a specified value of) the Riemann zeta function, such as in an equation. countable,usually
    — 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.

词形变化

Riemann zeta functions plural Riemann zeta-function alternative Riemann's zeta function alternative

词源

Named after German mathematician Bernhard Riemann.
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