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36 relations: Affine Lie algebra, Algebraic character, Algebraic number, Chowla–Selberg formula, Complex number, Dedekind sum, Dirichlet character, Euler function, Functional equation, Graduate Texts in Mathematics, Holomorphic function, Integer, Jacobi triple product, Karl Weierstrass, Kronecker limit formula, Leech lattice, Mathematics, Metaplectic group, Modular form, Modular group, Neal Koblitz, Nome (mathematics), Number theory, Partition (number theory), Pentagonal number theorem, Power series, Q-analog, Q-Pochhammer symbol, Ramanujan–Sato series, Richard Dedekind, Theta function, Upper half-plane, Weierstrass's elliptic functions, Weight (representation theory), Weyl character formula, 24 (number).
Affine Lie algebra
In mathematics, an affine Lie algebra is an infinite-dimensional Lie algebra that is constructed in a canonical fashion out of a finite-dimensional simple Lie algebra.
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Algebraic character
Algebraic character is a formal expression attached to a module in representation theory of semisimple Lie algebras that generalizes the character of a finite-dimensional representation and is analogous to the Harish-Chandra character of the representations of semisimple Lie groups.
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Algebraic number
An algebraic number is any complex number (including real numbers) that is a root of a non-zero polynomial (that is, a value which causes the polynomial to equal 0) in one variable with rational coefficients (or equivalently – by clearing denominators – with integer coefficients).
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Chowla–Selberg formula
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.
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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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Dedekind sum
In mathematics, Dedekind sums are certain sums of products of a sawtooth function, and are given by a function D of three integer variables.
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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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Euler function
In mathematics, the Euler function is given by Named after Leonhard Euler, it is a model example of a q-series, a modular form, and provides the prototypical example of a relation between combinatorics and complex analysis.
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Functional equation
In mathematics, a functional equation is any equation in which the unknown represents a function.
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Graduate Texts in Mathematics
Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag.
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Holomorphic function
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain.
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Integer
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
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Jacobi triple product
In mathematics, the Jacobi triple product is the mathematical identity: \left(1 - x^\right) \left(1 + x^ y^2\right) \left(1 +\frac\right).
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Karl Weierstrass
Karl Theodor Wilhelm Weierstrass (Weierstraß; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern analysis".
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Kronecker limit formula
In mathematics, the classical Kronecker limit formula describes the constant term at s.
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Leech lattice
In mathematics, the Leech lattice is an even unimodular lattice Λ24 in 24-dimensional Euclidean space, which is one of the best models for the kissing number problem.
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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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Metaplectic group
In mathematics, the metaplectic group Mp2n is a double cover of the symplectic group Sp2n.
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Modular form
In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition.
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Modular group
In mathematics, the modular group is the projective special linear group PSL(2,Z) of 2 x 2 matrices with integer coefficients and unit determinant.
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Neal Koblitz
Neal I. Koblitz (born December 24, 1948) is a Professor of Mathematics at the University of Washington.
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Nome (mathematics)
In mathematics, specifically the theory of elliptic functions, the nome is a special function and is given by.
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Number theory
Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.
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Partition (number theory)
In number theory and combinatorics, a partition of a positive integer n, also called an integer partition, is a way of writing n as a sum of positive integers.
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Pentagonal number theorem
In mathematics, the pentagonal number theorem, originally due to Euler, relates the product and series representations of the Euler function.
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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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Q-analog
In mathematics, a q-analog of a theorem, identity or expression is a generalization involving a new parameter q that returns the original theorem, identity or expression in the limit as.
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Q-Pochhammer symbol
In mathematics, in the area of combinatorics, a q-Pochhammer symbol, also called a q-shifted factorial, is a ''q''-analog of the Pochhammer symbol.
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Ramanujan–Sato series
In mathematics, a Ramanujan–Sato seriesHeng Huat Chan, Song Heng Chan, and Zhiguo Liu, "Domb's numbers and Ramanujan–Sato type series for 1/Pi" (2004)Gert Almkvist and Jesus Guillera, Ramanujan–Sato Like Series (2012) generalizes Ramanujan’s pi formulas such as, to the form by using other well-defined sequences of integers s(k) obeying a certain recurrence relation, sequences which may be expressed in terms of binomial coefficients \tbinom, and A,B,C employing modular forms of higher levels.
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Richard Dedekind
Julius Wilhelm Richard Dedekind (6 October 1831 – 12 February 1916) was a German mathematician who made important contributions to abstract algebra (particularly ring theory), axiomatic foundation for the natural numbers, algebraic number theory and the definition of the real numbers.
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Theta function
In mathematics, theta functions are special functions of several complex variables.
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Upper half-plane
In mathematics, the upper half-plane H is the set of complex numbers with positive imaginary part: The term arises from a common visualization of the complex number x + iy as the point (x,y) in the plane endowed with Cartesian coordinates.
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Weierstrass's elliptic functions
In mathematics, Weierstrass's elliptic functions are elliptic functions that take a particularly simple form; they are named for Karl Weierstrass.
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Weight (representation theory)
In the mathematical field of representation theory, a weight of an algebra A over a field F is an algebra homomorphism from A to F, or equivalently, a one-dimensional representation of A over F. It is the algebra analogue of a multiplicative character of a group.
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Weyl character formula
In mathematics, the Weyl character formula in representation theory describes the characters of irreducible representations of compact Lie groups in terms of their highest weights.
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24 (number)
24 (twenty-four) is the natural number following 23 and preceding 25.
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Redirects here:
Dedekind eta-function, Eta-quotient.
References
[1] https://en.wikipedia.org/wiki/Dedekind_eta_function
