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40 relations: Algebraic K-theory, Analytic continuation, Analytic number theory, Artin L-function, Automorphic form, Automorphic L-function, Bernoulli number, Bryan John Birch, Complex plane, Conjecture, Convergent series, Dirichlet character, Dirichlet L-function, Dirichlet series, Elliptic curve, Euler product, Fractal dimension, Function (mathematics), Functional equation (L-function), Galois module, Generalized Riemann hypothesis, Global field, Half-space (geometry), Hasse–Weil zeta function, Hecke L-function, Infinite set, Langlands program, Mathematical object, Meromorphic function, Modularity theorem, P-adic L-function, Peter Swinnerton-Dyer, Quantum chaos, Random matrix, Riemann zeta function, Selberg class, Self-similarity, Shimizu L-function, Special values of L-functions, Zeros and poles.
Algebraic K-theory
Algebraic K-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory.
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Analytic continuation
In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of a given analytic function.
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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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Artin L-function
In mathematics, an Artin L-function is a type of Dirichlet series associated to a linear representation ρ of a Galois group G. These functions were introduced in the 1923 by Emil Artin, in connection with his research into class field theory.
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Automorphic form
In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group G to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup \Gamma \subset G of the topological group.
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Automorphic L-function
In mathematics, an automorphic L-function is a function L(s,π,r) of a complex variable s, associated to an automorphic form π of a reductive group G over a global field and a finite-dimensional complex representation r of the Langlands dual group LG of G, generalizing the Dirichlet L-series of a Dirichlet character and the Mellin transform of a modular form.
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Bernoulli number
In mathematics, the Bernoulli numbers are a sequence of rational numbers which occur frequently in number theory.
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Bryan John Birch
Bryan John Birch F.R.S. (born 25 September 1931) is a British mathematician.
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Complex plane
In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis.
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Conjecture
In mathematics, a conjecture is a conclusion or proposition based on incomplete information, for which no proof has been found.
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Convergent series
In mathematics, a series is the sum of the terms of an infinite sequence of numbers.
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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 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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Dirichlet series
In mathematics, a Dirichlet series is any series of the form where s is complex, and a_n is a complex sequence.
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Elliptic curve
In mathematics, an elliptic curve is a plane algebraic curve defined by an equation of the form which is non-singular; that is, the curve has no cusps or self-intersections.
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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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Fractal dimension
In mathematics, more specifically in fractal geometry, a fractal dimension is a ratio providing a statistical index of complexity comparing how detail in a pattern (strictly speaking, a fractal pattern) changes with the scale at which it is measured.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Functional equation (L-function)
In mathematics, the L-functions of number theory are expected to have several characteristic properties, one of which is that they satisfy certain functional equations.
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Galois module
In mathematics, a Galois module is a ''G''-module, with G being the Galois group of some extension of fields.
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Generalized Riemann hypothesis
The Riemann hypothesis is one of the most important conjectures in mathematics.
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Global field
In mathematics, a global field is a field that is either.
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Half-space (geometry)
In geometry, a half-space is either of the two parts into which a plane divides the three-dimensional Euclidean space.
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Hasse–Weil zeta function
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.
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Hecke L-function
In mathematics, a Hecke L-function may refer to.
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Infinite set
In set theory, an infinite set is a set that is not a finite set.
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Langlands program
In mathematics, the Langlands program is a web of far-reaching and influential conjectures about connections between number theory and geometry.
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Mathematical object
A mathematical object is an abstract object arising in mathematics.
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Meromorphic function
In the mathematical field of complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all of D except for a discrete set of isolated points, which are poles of the function.
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Modularity theorem
In mathematics, the modularity theorem (formerly called the Taniyama–Shimura conjecture or related names like Taniyama–Shimura–Weil conjecture due to rediscovery) states that elliptic curves over the field of rational numbers are related to modular forms.
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P-adic L-function
In mathematics, a p-adic zeta function, or more generally a p-adic L-function, is a function analogous to the Riemann zeta function, or more general ''L''-functions, but whose domain and target are p-adic (where p is a prime number).
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Peter Swinnerton-Dyer
Sir Henry Peter Francis Swinnerton-Dyer, 16th Baronet (born 2 August 1927), commonly known as Peter Swinnerton-Dyer, is an English mathematician specialising in number theory at University of Cambridge.
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Quantum chaos
Quantum chaos is a branch of physics which studies how chaotic classical dynamical systems can be described in terms of quantum theory.
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Random matrix
In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all elements are random variables.
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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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Self-similarity
In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e. the whole has the same shape as one or more of the parts).
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Shimizu L-function
In mathematics, the Shimizu L-function, introduced by, is a Dirichlet series associated to a totally real algebraic number field.
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Special values of L-functions
In mathematics, the study of special values of L-functions is a subfield of number theory devoted to generalising formulae such as the Leibniz formula for pi, namely by the recognition that expression on the left-hand side is also L(1) where L(s) is the Dirichlet L-function for the Gaussian field.
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Zeros and poles
In mathematics, a zero of a function is a value such that.
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Redirects here:
L function, L-function of an elliptic curve, L-functions.
References
[1] https://en.wikipedia.org/wiki/L-function
