In mathematics, a Dedekind cut, named after Richard Dedekind, is a partition of the rational numbers into two non-empty parts A and B, such that all elements of A are less than all elements of B, and A contains no greatest element.

In mathematics, the extent to which unique factorization fails in the ring of integers of an algebraic number field ( or more generally any Dedekind domain ) can be described by a certain group known as an ideal class group ( or class group ).

Although the formalisation of logic was much advanced by the work of such figures as Gottlob Frege, Giuseppe Peano, Bertrand Russell, and Richard Dedekind, the story of modern proof theory is often seen as being established by David Hilbert, who initiated what is called Hilbert's program in the foundations of mathematics.

Dedekind, who felt that there were significant gaps at the time in his mathematics education, considered that the occasion to study with Dirichlet made him " a new human being ".

The use of multisets in mathematics predates the name " multiset " by nearly 90 years: Richard Dedekind used multisets in a paper published in 1888.

In mathematics, in particular commutative algebra, the concept of fractional ideal is introduced in the context of integral domains and is particularly fruitful in the study of Dedekind domains.

In mathematics, the Chowla – Selberg formula is the evaluation of a certain product of values of the Gamma function at rational values in terms of values of the Dedekind eta function at imaginary quadratic irrational numbers.

In mathematics, Dedekind sums, named after Richard Dedekind, are certain sums of products of a sawtooth function, and are given by a function D of three integer variables.

In mathematics, a zeta function is ( usually ) a function analogous to the original example: the Riemann zeta function

* The symmetric function equation of the Riemann zeta function in mathematics, also known as the Riemann Xi function

* The Riemann zeta function in mathematics

In mathematics, the Bernoulli polynomials occur in the study of many special functions and in particular the Riemann zeta function and the Hurwitz zeta function.

The Riemann hypothesis, one of the most important unsolved problems in mathematics, concerns the location of the zeros of the Riemann zeta function.

In mathematics, the Hurwitz zeta function, named after Adolf Hurwitz, is one of the many zeta functions.

The Riemann zeta function is one of the most important functions in mathematics, because of its relationship to the distribution of the prime numbers.

In mathematics, the Hasse – Weil zeta function attached to an algebraic variety V defined over an algebraic number field K is one of the two most important types of L-function.

In mathematics, the Artin – Mazur zeta function, named after Michael Artin and Barry Mazur, is a tool for studying the iterated functions that occur in dynamical systems and fractals.

In mathematics, the Ihara zeta-function is a zeta function associated with a finite graph.

In mathematics, the Gauss – Kuzmin – Wirsing operator, named after Carl Gauss, Rodion Osievich Kuzmin and Eduard Wirsing, occurs in the study of continued fractions ; it is also related to the Riemann zeta function.

In mathematics, the Lindelöf hypothesis is a conjecture by Finnish mathematician Ernst Leonard Lindelöf ( see ) about the rate of growth of the Riemann zeta function on the critical line that is implied by the Riemann hypothesis.

In mathematics, the Stieltjes constants are the numbers that occur in the Laurent series expansion of the Riemann zeta function:

In mathematics, a rational zeta series is the representation of an arbitrary real number in terms of a series consisting of rational numbers and the Riemann zeta function or the Hurwitz zeta function.

In mathematics, the explicit formula for L-functions are relations between sums over the complex number zeroes of an L-function and sums over prime powers, introduced by for the Riemann zeta function.

In mathematics, the Dirichlet beta function ( also known as the Catalan beta function ) is a special function, closely related to the Riemann zeta function.

In mathematics, a zeta constant is a number obtained by plugging an integer into the Riemann zeta function.

:" A choice function exists in constructive mathematics, because a choice is implied by the very meaning of existence.

* Ai ( x ), the Airy function, a special function in mathematics

* Binary function, a function in mathematics that takes two arguments

In mathematics, a binary function, or function of two variables, is a function which takes two inputs.

In mathematics, the Borsuk – Ulam theorem, named after Stanisław Ulam and Karol Borsuk, states that every continuous function from an n-sphere into Euclidean n-space maps some pair of antipodal points to the same point.

In chemistry, physics, and mathematics, the Boltzmann distribution ( also called the Gibbs Distribution ) is a certain distribution function or probability measure for the distribution of the states of a system.

* Partition function ( mathematics )

In mathematics, a bilinear operator is a function combining elements of two vector spaces to yield an element of a third vector space that is linear in each of its arguments.

In mathematics, a continuous function is a function for which, intuitively, " small " changes in the input result in " small " changes in the output.

In mathematics, a contraction mapping, or contraction, on a metric space ( M, d ) is a function f from M to itself, with the property that there is some nonnegative real number < math > k < 1 </ math > such that for all x and y in M,

A convex function | function is convex if and only if its Epigraph ( mathematics ) | epigraph, the region ( in green ) above its graph of a function | graph ( in blue ), is a convex set.

In mathematics and computer science, currying is the technique of transforming a function that takes multiple arguments ( or an n-tuple of arguments ) in such a way that it can be called as a chain of functions each with a single argument ( partial application ).

In mathematics and, in particular, functional analysis, convolution is a mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions, giving the area overlap between the two functions as a function of the amount that one of the original functions is translated.

In mathematics, the Cauchy – Riemann differential equations in complex analysis, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which must be satisfied if we know that a complex function is complex differentiable.

In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes.

* The Dirac delta function in mathematics

A drawing for a booster engine for steam locomotive s. Engineering is applied to design, with emphasis on function and the utilization of mathematics and science.