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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 article "Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse" (usual English translation: "On the Number of Primes Less Than a Given Magnitude") is a seminal 9-page paper by Bernhard Riemann published in the November 1859 edition of the Monatsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin.
The uppercase zeta is not used, because it is normally identical to Latin Z. The lower case letter can be used to represent: The Riemann zeta function in mathematics [3] The Hurwitz Zeta Function in mathematics [4] The Weierstrass zeta-function [5] The damping ratio of an oscillating system in engineering and physics [6]
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.
He is mostly recognized for the Matsumoto zeta function, a zeta function named after him. He co-edited Analytic Number Theory (2002), a book about prime numbers , divisor problems, Diophantine equations , and other topics related to analytic number theory , including Diophantine approximations, and the theory of zeta and L-functions. [ 3 ]
In mathematics, the Lindelöf hypothesis is a conjecture by Finnish mathematician Ernst Leonard Lindelöf [1] about the rate of growth of the Riemann zeta function on the critical line. This hypothesis is implied by the Riemann hypothesis .
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 ...
Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics (2003) is a historical book on mathematics by John Derbyshire, detailing the history of the Riemann hypothesis, named for Bernhard Riemann, and some of its applications. The book was awarded the Mathematical Association of America's inaugural Euler Book Prize in ...