Table of Contents
13 relations: Artin reciprocity, Betti's theorem, Cubic reciprocity, Frobenius reciprocity, Quadratic reciprocity, Quartic reciprocity, Reciprocity, Reciprocity (electrical networks), Reciprocity (electromagnetism), Reciprocity (engineering), Stanley's reciprocity theorem, Tellegen's theorem, Weil reciprocity law.
Artin reciprocity
The Artin reciprocity law, which was established by Emil Artin in a series of papers (1924; 1927; 1930), is a general theorem in number theory that forms a central part of global class field theory.
See Reciprocity theorem and Artin reciprocity
Betti's theorem
Betti's theorem, also known as Maxwell–Betti reciprocal work theorem, discovered by Enrico Betti in 1872, states that for a linear elastic structure subject to two sets of forces i.
See Reciprocity theorem and Betti's theorem
Cubic reciprocity
Cubic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x3 ≡ p (mod q) is solvable; the word "reciprocity" comes from the form of the main theorem, which states that if p and q are primary numbers in the ring of Eisenstein integers, both coprime to 3, the congruence x3 ≡ p (mod q) is solvable if and only if x3 ≡ q (mod p) is solvable.
See Reciprocity theorem and Cubic reciprocity
Frobenius reciprocity
In mathematics, and in particular representation theory, Frobenius reciprocity is a theorem expressing a duality between the process of restricting and inducting.
See Reciprocity theorem and Frobenius reciprocity
Quadratic reciprocity
In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers.
See Reciprocity theorem and Quadratic reciprocity
Quartic reciprocity
Quartic or biquadratic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x4 ≡ p (mod q) is solvable; the word "reciprocity" comes from the form of some of these theorems, in that they relate the solvability of the congruence x4 ≡ p (mod q) to that of x4 ≡ q (mod p).
See Reciprocity theorem and Quartic reciprocity
Reciprocity
Reciprocity may refer to.
See Reciprocity theorem and Reciprocity
Reciprocity (electrical networks)
Reciprocity in electrical networks is a property of a circuit that relates voltages and currents at two points.
See Reciprocity theorem and Reciprocity (electrical networks)
Reciprocity (electromagnetism)
In classical electromagnetism, reciprocity refers to a variety of related theorems involving the interchange of time-harmonic electric current densities (sources) and the resulting electromagnetic fields in Maxwell's equations for time-invariant linear media under certain constraints.
See Reciprocity theorem and Reciprocity (electromagnetism)
Reciprocity (engineering)
Reciprocity in linear systems is the principle that a response Rab, measured at a location (and direction if applicable) a, when the system has an excitation signal applied at a location (and direction if applicable) b, is exactly equal to Rba which is the response at location b, when that same excitation is applied at a.
See Reciprocity theorem and Reciprocity (engineering)
Stanley's reciprocity theorem
In combinatorial mathematics, Stanley's reciprocity theorem, named after MIT mathematician Richard P. Stanley, states that a certain functional equation is satisfied by the generating function of any rational cone (defined below) and the generating function of the cone's interior.
See Reciprocity theorem and Stanley's reciprocity theorem
Tellegen's theorem
Tellegen's theorem is one of the most powerful theorems in network theory.
See Reciprocity theorem and Tellegen's theorem
Weil reciprocity law
In mathematics, the Weil reciprocity law is a result of André Weil holding in the function field K(C) of an algebraic curve C over an algebraically closed field K. Given functions f and g in K(C), i.e. rational functions on C, then where the notation has this meaning: (h) is the divisor of the function h, or in other words the formal sum of its zeroes and poles counted with multiplicity; and a function applied to a formal sum means the product (with multiplicities, poles counting as a negative multiplicity) of the values of the function at the points of the divisor.
See Reciprocity theorem and Weil reciprocity law
References
Also known as Reciprocity theorem (disambiguation).