arithmetic function

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• Arithmetic function — In number theory, an arithmetic (or arithmetical) function is a real or complex valued function ƒ(n) defined on the set of natural numbers (i.e. positive integers) that expresses some arithmetical property of n. [1] An example of an arithmetic… …   Wikipedia

• arithmetic function —       any mathematical function defined for integers (…, −3, −2, −1, 0, 1, 2, 3, …) and dependent upon those properties of the integer itself as a number, in contrast to functions that are defined for other values (real numbers (real number),… …   Universalium

• arithmetic function — noun Any function that is defined for all positive integers, and has values that are either real or complex …   Wiktionary

• Extremal orders of an arithmetic function — In mathematics, in number theory, the extremal orders of an arithmetic function are best possible bounds of the given arithmetic function. Specifically, if f(n) is an arithmetic function and m(n) is a non decreasing function that is ultimately… …   Wikipedia

• Normal order of an arithmetic function — In number theory, the normal order of an arithmetic function is some simpler or better understood function which usually takes the same or closely approximate values. Let ƒ be a function on the natural numbers. We say that the normal order of ƒ… …   Wikipedia

• Average order of an arithmetic function — In number theory, the average order of an arithmetic function is some simpler or better understood function which takes the same values on average .Let f be an arithmetic function. We say that the average order of f is g if : sum {n le x} f(n)… …   Wikipedia

• Arithmetic dynamics — is a new field that is an amalgamation of two areas of mathematics, dynamical systems and number theory. The subject can be viewed as the transfer of previous results in the theory of Diophantine equations to the setting of discrete dynamical… …   Wikipedia

• Function (mathematics) — f(x) redirects here. For the band, see f(x) (band). Graph of example function, In mathematics, a function associates one quantity, the a …   Wikipedia

• Arithmetic derivative — In number theory, the arithmetic derivative, or number derivative, is a function defined for integers, based on prime factorization, by analogy with the product rule for the derivative of a function that is used in mathematical analysis. Contents …   Wikipedia

• Arithmetic of abelian varieties — In mathematics, the arithmetic of abelian varieties is the study of the number theory of an abelian variety, or family of those. It goes back to the studies of Fermat on what are now recognised as elliptic curves; and has become a very… …   Wikipedia

• Arithmetic shift — In computer programming, an arithmetic shift is a shift operator, sometimes known as a signed shift (though it is not restricted to signed operands). For binary numbers it is a bitwise operation that shifts all of the bits of its operand; every… …   Wikipedia