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The Riemann zeta function ζ(z) plotted with domain coloring. [1] The pole at = and two zeros on the critical line.. The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter ζ (), is a mathematical function of a complex variable defined as () = = = + + + for >, and its analytic continuation elsewhere.
Minakshisundaram–Pleijel zeta function of a Laplacian; Motivic zeta function of a motive; Multiple zeta function, or Mordell–Tornheim zeta function of several variables; p-adic zeta function of a p-adic number; Prime zeta function, like the Riemann zeta function, but only summed over primes; Riemann zeta function, the archetypal example ...
Usage on ja.wikipedia.org 与えられた数より小さい素数の個数について; Usage on lt.wikipedia.org Rymano dzeta funkcija; Usage on nl.wikipedia.org Über die Anzahl der Primzahlen unter einer gegebenen Grösse; Usage on no.wikipedia.org Riemanns zetafunksjon; Usage on pl.wikipedia.org Funkcja dzeta Riemanna; Usage on sl.wikipedia.org
The zeta function values listed below include function values at the negative even numbers (s = −2, −4, etc.), for which ζ(s) = 0 and which make up the so-called trivial zeros. The Riemann zeta function article includes a colour plot illustrating how the function varies over a continuous rectangular region of the complex plane.
Zeta functions and L-functions express important relations between the geometry of Riemann surfaces, number theory and dynamical systems.Zeta functions, and their generalizations such as the Selberg class S, are conjectured to have various important properties, including generalizations of the Riemann hypothesis and various relationships with automorphic forms as well as to the representations ...
In mathematics, the Jacobi zeta function Z(u) is the logarithmic derivative of the Jacobi theta function Θ(u). It is also commonly denoted as zn ( u , k ) {\displaystyle \operatorname {zn} (u,k)} [ 1 ]
Upload file; Search. Search. Appearance. Donate; ... Download as PDF; Printable version; ... In mathematics, Matsumoto zeta functions are a type of zeta function ...
The Minakshisundaram–Pleijel zeta function is an example, when the operator is the Laplacian of a compact Riemannian manifold. One of the most important motivations for Arakelov theory is the zeta functions for operators with the method of heat kernels generalized algebro-geometrically.