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39 relations: Absolute convergence, Analytic function, Analytic number theory, Bounded function, Cambridge University Press, Completely multiplicative function, Complex number, Dirichlet character, Dirichlet convolution, Dirichlet L-function, Divisor function, Euler product, Euler's totient function, Fiber (mathematics), General Dirichlet series, Generalized Riemann hypothesis, Generating function, Jordan's totient function, Liouville function, Logarithmic derivative, Mathematics, Möbius function, Möbius inversion formula, Mellin inversion theorem, Perron's formula, Peter Gustav Lejeune Dirichlet, Pointwise, Power series, Prime omega function, Radius of convergence, Ramanujan's sum, Riemann zeta function, Selberg class, Sequence, Series (mathematics), Summation by parts, Uniform convergence, Von Mangoldt function, Zeta function regularization.
Absolute convergence
In mathematics, an infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute values of the summands is finite.
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Analytic function
In mathematics, an analytic function is a function that is locally given by a convergent power series.
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Analytic number theory
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers.
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Bounded function
In mathematics, a function f defined on some set X with real or complex values is called bounded, if the set of its values is bounded.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Completely multiplicative function
In number theory, functions of positive integers which respect products are important and are called completely multiplicative functions or totally multiplicative functions.
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Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
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Dirichlet character
In number theory, Dirichlet characters are certain arithmetic functions which arise from completely multiplicative characters on the units of \mathbb Z / k \mathbb Z. Dirichlet characters are used to define Dirichlet ''L''-functions, which are meromorphic functions with a variety of interesting analytic properties.
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Dirichlet convolution
In mathematics, the Dirichlet convolution is a binary operation defined for arithmetic functions; it is important in number theory.
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Dirichlet L-function
In mathematics, a Dirichlet L-series is a function of the form Here χ is a Dirichlet character and s a complex variable with real part greater than 1.
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Divisor function
In mathematics, and specifically in number theory, a divisor function is an arithmetic function related to the divisors of an integer.
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Euler product
In number theory, an Euler product is an expansion of a Dirichlet series into an infinite product indexed by prime numbers.
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Euler's totient function
In number theory, Euler's totient function counts the positive integers up to a given integer that are relatively prime to.
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Fiber (mathematics)
In mathematics, the term fiber (or fibre in British English) can have two meanings, depending on the context.
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General Dirichlet series
In the field of mathematical analysis, a general Dirichlet series is an infinite series that takes the form of where a_n, s are complex numbers and \ is a strictly increasing sequence of nonnegative real numbers that tends to infinity.
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Generalized Riemann hypothesis
The Riemann hypothesis is one of the most important conjectures in mathematics.
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Generating function
In mathematics, a generating function is a way of encoding an infinite sequence of numbers (an) by treating them as the coefficients of a power series.
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Jordan's totient function
Let k be a positive integer.
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Liouville function
The Liouville function, denoted by λ(n) and named after Joseph Liouville, is an important function in number theory.
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Logarithmic derivative
In mathematics, specifically in calculus and complex analysis, the logarithmic derivative of a function f is defined by the formula where f' is the derivative of f. Intuitively, this is the infinitesimal relative change in f; that is, the infinitesimal absolute change in f, namely f', scaled by the current value of f. When f is a function f(x) of a real variable x, and takes real, strictly positive values, this is equal to the derivative of ln(f), or the natural logarithm of f. This follows directly from the chain rule.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Möbius function
The classical Möbius function is an important multiplicative function in number theory and combinatorics.
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Möbius inversion formula
In mathematics, the classic Möbius inversion formula was introduced into number theory during the 19th century by August Ferdinand Möbius.
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Mellin inversion theorem
In mathematics, the Mellin inversion formula (named after Hjalmar Mellin) tells us conditions under which the inverse Mellin transform, or equivalently the inverse two-sided Laplace transform, are defined and recover the transformed function.
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Perron's formula
In mathematics, and more particularly in analytic number theory, Perron's formula is a formula due to Oskar Perron to calculate the sum of an arithmetical function, by means of an inverse Mellin transform.
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Peter Gustav Lejeune Dirichlet
Johann Peter Gustav Lejeune Dirichlet (13 February 1805 – 5 May 1859) was a German mathematician who made deep contributions to number theory (including creating the field of analytic number theory), and to the theory of Fourier series and other topics in mathematical analysis; he is credited with being one of the first mathematicians to give the modern formal definition of a function.
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Pointwise
In mathematics, the qualifier pointwise is used to indicate that a certain property is defined by considering each value f(x) of some function f. An important class of pointwise concepts are the pointwise operations — operations defined on functions by applying the operations to function values separately for each point in the domain of definition.
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Power series
In mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the nth term and c is a constant.
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Prime omega function
In number theory, the prime omega function \omega(n) counts the number of distinct prime factors of a natural number n, where the related function \Omega(n) counts the total number of prime factors of n counting multiplicity (see arithmetic function).
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Radius of convergence
In mathematics, the radius of convergence of a power series is the radius of the largest disk in which the series converges.
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Ramanujan's sum
In number theory, a branch of mathematics, Ramanujan's sum, usually denoted cq(n), is a function of two positive integer variables q and n defined by the formula: where (a, q).
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Riemann zeta function
The Riemann zeta function or Euler–Riemann zeta function,, is a function of a complex variable s that analytically continues the sum of the Dirichlet series which converges when the real part of is greater than 1.
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Selberg class
In mathematics, the Selberg class is an axiomatic definition of a class of ''L''-functions.
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Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.
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Series (mathematics)
In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity.
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Summation by parts
In mathematics, summation by parts transforms the summation of products of sequences into other summations, often simplifying the computation or (especially) estimation of certain types of sums.
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Uniform convergence
In the mathematical field of analysis, uniform convergence is a type of convergence of functions stronger than pointwise convergence.
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Von Mangoldt function
In mathematics, the von Mangoldt function is an arithmetic function named after German mathematician Hans von Mangoldt.
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Zeta function regularization
In mathematics and theoretical physics, zeta function regularization is a type of regularization or summability method that assigns finite values to divergent sums or products, and in particular can be used to define determinants and traces of some self-adjoint operators.
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Redirects here:
Dirichlet polynomial, Formal Dirichlet series.
References
[1] https://en.wikipedia.org/wiki/Dirichlet_series
