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14 relations: Eigenvalues and eigenvectors, Frobenius endomorphism, Goro Shimura, Hasse–Weil zeta function, Hecke operator, Ilya Piatetski-Shapiro, Langlands program, Local zeta-function, Mellin transform, Modular curve, Modular form, Number theory, Prime number, Shimura variety.
Eigenvalues and eigenvectors
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.
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Frobenius endomorphism
In commutative algebra and field theory, the Frobenius endomorphism (after Ferdinand Georg Frobenius) is a special endomorphism of commutative rings with prime characteristic, an important class which includes finite fields.
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Goro Shimura
is a Japanese mathematician, and currently a professor emeritus of mathematics (former Michael Henry Strater Chair) at Princeton University.
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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 operator
In mathematics, in particular in the theory of modular forms, a Hecke operator, studied by, is a certain kind of "averaging" operator that plays a significant role in the structure of vector spaces of modular forms and more general automorphic representations.
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Ilya Piatetski-Shapiro
Ilya Piatetski-Shapiro (Hebrew: איליה פיאטצקי-שפירו; Илья́ Ио́сифович Пяте́цкий-Шапи́ро; 30 March 1929 – 21 February 2009) was a Soviet-born Israeli mathematician.
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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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Local zeta-function
In number theory, the local zeta function Z(V,s) (sometimes called the congruent zeta function) is defined as where N_m is the number of points of V defined over the degree m extension \mathbf_ of \mathbf_q, and V is a non-singular n-dimensional projective algebraic variety over the field \mathbf_q with q elements.
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Mellin transform
In mathematics, the Mellin transform is an integral transform that may be regarded as the multiplicative version of the two-sided Laplace transform.
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Modular curve
In number theory and algebraic geometry, a modular curve Y(Γ) is a Riemann surface, or the corresponding algebraic curve, constructed as a quotient of the complex upper half-plane H by the action of a congruence subgroup Γ of the modular group of integral 2×2 matrices SL(2, Z).
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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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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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Prime number
A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
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Shimura variety
In number theory, a Shimura variety is a higher-dimensional analogue of a modular curve that arises as a quotient of a Hermitian symmetric space by a congruence subgroup of a reductive algebraic group defined over Q. The term "Shimura variety" applies to the higher-dimensional case, in the case of one-dimensional varieties one speaks of Shimura curves.
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References
[1] https://en.wikipedia.org/wiki/Eichler–Shimura_congruence_relation
