Reciprocity theorem
Encyclopedia
Reciprocity theorem may refer to:
- Quadratic reciprocityQuadratic reciprocityIn number theory, the law of quadratic reciprocity is a theorem about modular arithmetic which gives conditions for the solvability of quadratic equations modulo prime numbers...
, a theorem about modular arithmetic- Cubic reciprocityCubic reciprocityCubic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x3 ≡ p 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...
- Quartic reciprocityQuartic reciprocityQuartic or biquadratic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x4 ≡ p is solvable; the word "reciprocity" comes from the form of some of these theorems, in that they relate the solvability of the...
- Artin reciprocityArtin reciprocityThe Artin reciprocity law, established by Emil Artin in a series of papers , is a general theorem in number theory that forms a central part of the global class field theory...
- Weil reciprocity for algebraic curves
- Cubic reciprocity
- Frobenius reciprocity theorem for group representations
- Stanley's reciprocity theoremStanley's reciprocity theoremIn 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 and the generating function of the cone's interior.A rational cone is the set of all...
for generating functions - Reciprocity (electromagnetism)Reciprocity (electromagnetism)In classical electromagnetism, reciprocity refers to a variety of related theorems involving the interchange of time-harmonic electric current densities and the resulting electromagnetic fields in Maxwell's equations for time-invariant linear media under certain constraints...
, theorems relating sources and the resulting fields in classical electromagnetism - Tellegen's theoremTellegen's theoremTellegen's theorem is one of the most powerful theorems in network theory. Most of the energy distribution theorems and extremum principles in network theory can be derived from it. It was published in 1952 by Bernard Tellegen...
, a theorem about the transfer function of passive networks - Reciprocity law for Dedekind sums