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46 relations: Absolute value (algebra), Adele ring, Adelic algebraic group, Alexander Ostrowski, Algebraic equation, André Weil, Cambridge University Press, Chinese remainder theorem, Claude Chevalley, Commutative ring, Completion (algebra), Continuous function, Convex set, Crelle's Journal, Diophantine approximation, Diophantine equation, Diophantine geometry, Field (mathematics), Finite difference, Functional analysis, Hahn–Banach theorem, Helmut Hasse, If and only if, Integer, Kurt Hensel, Kurt Mahler, Lift (mathematics), Locally compact group, Locally compact space, Mathematical analysis, Mathematics, Modular arithmetic, Newton's method, Number theory, P-adic number, P-adic quantum mechanics, Polynomial, Prime number, Quantum mechanics, Rational number, Real analysis, Real number, Series (mathematics), Spectral theory, Topological vector space, Ultrametric space.
Absolute value (algebra)
In mathematics, an absolute value is a function which measures the "size" of elements in a field or integral domain.
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Adele ring
In mathematics, the adele ring (also adelic ring or ring of adeles) is defined in class field theory, a branch of algebraic number theory.
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Adelic algebraic group
In abstract algebra, an adelic algebraic group is a semitopological group defined by an algebraic group G over a number field K, and the adele ring A.
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Alexander Ostrowski
Alexander Markowich Ostrowski (Олександр Маркович Островський; Алекса́ндр Ма́ркович Остро́вский; 25 September 1893, in Kiev, Russian Empire – 20 November 1986, in Montagnola, Lugano, Switzerland) was a mathematician.
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Algebraic equation
In mathematics, an algebraic equation or polynomial equation is an equation of the form where P and Q are polynomials with coefficients in some field, often the field of the rational numbers.
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André Weil
André Weil (6 May 1906 – 6 August 1998) was an influential French mathematician of the 20th century, known for his foundational work in number theory, algebraic geometry.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Chinese remainder theorem
The Chinese remainder theorem is a theorem of number theory, which states that if one knows the remainders of the Euclidean division of an integer by several integers, then one can determine uniquely the remainder of the division of by the product of these integers, under the condition that the divisors are pairwise coprime.
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Claude Chevalley
Claude Chevalley (11 February 1909 – 28 June 1984) was a French mathematician who made important contributions to number theory, algebraic geometry, class field theory, finite group theory, and the theory of algebraic groups.
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Commutative ring
In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative.
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Completion (algebra)
In abstract algebra, a completion is any of several related functors on rings and modules that result in complete topological rings and modules.
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Continuous function
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
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Convex set
In convex geometry, a convex set is a subset of an affine space that is closed under convex combinations.
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Crelle's Journal
Crelle's Journal, or just Crelle, is the common name for a mathematics journal, the Journal für die reine und angewandte Mathematik (in English: Journal for Pure and Applied Mathematics).
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Diophantine approximation
In number theory, the field of Diophantine approximation deals with the approximation of real numbers by rational numbers.
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Diophantine equation
In mathematics, a Diophantine equation is a polynomial equation, usually in two or more unknowns, such that only the integer solutions are sought or studied (an integer solution is a solution such that all the unknowns take integer values).
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Diophantine geometry
In mathematics, diophantine geometry is one approach to the theory of Diophantine equations, formulating questions about such equations in terms of algebraic geometry over a ground field K that is not algebraically closed, such as the field of rational numbers or a finite field, or more general commutative ring such as the integers.
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Field (mathematics)
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.
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Finite difference
A finite difference is a mathematical expression of the form.
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Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense.
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Hahn–Banach theorem
In mathematics, the Hahn–Banach theorem is a central tool in functional analysis.
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Helmut Hasse
Helmut Hasse (25 August 1898 – 26 December 1979) was a German mathematician working in algebraic number theory, known for fundamental contributions to class field theory, the application of p-adic numbers to local class field theory and diophantine geometry (Hasse principle), and to local zeta functions.
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If and only if
In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.
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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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Kurt Hensel
Kurt Wilhelm Sebastian Hensel (29 December 1861 – 1 June 1941) was a German mathematician born in Königsberg.
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Kurt Mahler
Kurt Mahler FRS (26 July 1903, Krefeld, Germany – 25 February 1988, Canberra, Australia) was a mathematician.
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Lift (mathematics)
In the branch of mathematics called category theory, given a morphism f from an object X to an object Y, and a morphism g from an object Z to Y, a lift or lifting of f to Z is a morphism h from X to Z such that f.
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Locally compact group
In mathematics, a locally compact group is a topological group G for which the underlying topology is locally compact and Hausdorff.
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Locally compact space
In topology and related branches of mathematics, a topological space is called locally compact if, roughly speaking, each small portion of the space looks like a small portion of a compact space.
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Mathematical analysis
Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.
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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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Modular arithmetic
In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).
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Newton's method
In numerical analysis, Newton's method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function.
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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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P-adic number
In mathematics, the -adic number system for any prime number extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems.
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P-adic quantum mechanics
p-adic quantum mechanics is a collection of related research efforts in quantum physics that replace real numbers with ''p''-adic numbers.
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Polynomial
In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
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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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Quantum mechanics
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.
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Rational number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.
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Real analysis
In mathematics, real analysis is the branch of mathematical analysis that studies the behavior of real numbers, sequences and series of real numbers, and real-valued functions.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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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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Spectral theory
In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces.
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Topological vector space
In mathematics, a topological vector space (also called a linear topological space) is one of the basic structures investigated in functional analysis.
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Ultrametric space
In mathematics, an ultrametric space is a metric space in which the triangle inequality is strengthened to d(x,z)\leq\max\left\.
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P-adic calculus, Ultrametric analysis, Ultrametric calculus.
References
[1] https://en.wikipedia.org/wiki/P-adic_analysis
