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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.
The word zeta is the ancestor of zed, the name of the Latin letter Z in Commonwealth English. Swedish and many Romance languages (such as Italian and Spanish ) do not distinguish between the Greek and Roman forms of the letter; " zeta " is used to refer to the Roman letter Z as well as the Greek letter.
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.
The zeta function is also zero for other values of s, which are called nontrivial zeros. The Riemann hypothesis is concerned with the locations of these nontrivial zeros, and states that: The real part of every nontrivial zero of the Riemann zeta function is 1 / 2 .
Zeta Phi Beta Sorority, Inc. (ΖΦΒ) is an International collegiate sorority that is historically African American. In 1920, five women from Howard University envisioned a sorority that would raise the consciousness of their people, encourage the highest standards of scholastic achievement, and foster a greater sense of unity among its members.
The zeta potential is an important and readily measurable indicator of the stability of colloidal dispersions. The magnitude of the zeta potential indicates the degree of electrostatic repulsion between adjacent, similarly charged particles in a dispersion. For molecules and particles that are small enough, a high zeta potential will confer ...
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Unfortunately, extensive computer searching [8] has failed to find such a constant, and in fact it is now known that if exists and if it is an algebraic number of degree at most 25, then the coefficients in its minimal polynomial must be enormous, at least , so extending Apéry's proof to work on the higher odd zeta constants does not seem ...