Reciprocity - Mathematics

Mathematics

• Reciprocity law in mathematics, including
  • Quadratic reciprocity, a fundamental result in number theory
  • Cubic reciprocity, theorems that state conditions under which the congruence x3 ≡ p (mod q) is solvable
  • Quartic reciprocity, a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x4 ≡ p (mod q) is solvable
  • Artin reciprocity law, a general theorem in number theory that provided a partial solution to Hilbert's ninth problem
  • Reciprocity relation or exact differential, a mathematical differential of the form dQ, for some differentiable function Q
• Weil reciprocity for algebraic curves
• Reciprocal polynomials, the coefficients of the remainder polynomial are the bits of the CRC
• Reciprocal square root
• Reciprocity (projective geometry), a collineation from a projective space onto its dual space, taking points to hyperplanes (and vice versa) and preserving incidence
• Frobenius reciprocity, from group representation theory
• Reciprocity law for Dedekind sums
• Stanley's reciprocity theorem, 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
• Hermite reciprocity for invariants of binary forms.