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Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities. In these contexts, the capital letters and the small letters represent distinct and unrelated entities.
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 symmetric function equation of the Riemann zeta function in mathematics, also known as the Riemann Xi function; A universal set in set theory; A number used in the remainder term of Taylor's theorem that falls between the limits a and b
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.
Atle Selberg. In mathematics, the Selberg class is an axiomatic definition of a class of L-functions.The members of the class are Dirichlet series which obey four axioms that seem to capture the essential properties satisfied by most functions that are commonly called L-functions or zeta functions.
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
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Delta (/ ˈ d ɛ l t ə /; [1] uppercase Δ, lowercase δ; Greek: δέλτα, délta, ) [2] is the fourth letter of the Greek alphabet. In the system of Greek numerals , it has a value of four. It was derived from the Phoenician letter dalet 𐤃. [ 3 ]