reciprocity law
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1: 27.9 Quadratic Characters
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27.9.2
►If are distinct odd primes, then the quadratic reciprocity law states that
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►Both (27.9.1) and (27.9.2) are valid with replaced by ; the reciprocity law (27.9.3) holds if are replaced by any two relatively prime odd integers .
2: 25.16 Mathematical Applications
3: 36.6 Scaling Relations
§36.6 Scaling Relations
…4: 5.3 Graphics
5: Bibliography F
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On the reciprocal modulus relation for elliptic integrals.
SIAM J. Math. Anal. 1 (4), pp. 524–526.
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On the coefficients in the recursion formulae of orthogonal polynomials.
Proc. Roy. Irish Acad. Sect. A 76 (1), pp. 1–6.
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6: 8.23 Statistical Applications
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►In queueing theory the Erlang loss function is used, which can be expressed in terms of the reciprocal of ; see Jagerman (1974) and Cooper (1981, pp. 80, 316–319).
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7: 8.24 Physical Applications
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►The function appears in: discussions of power-law relaxation times in complex physical systems (Sornette (1998)); logarithmic oscillations in relaxation times for proteins (Metzler et al. (1999)); Gaussian orbitals and exponential (Slater) orbitals in quantum chemistry (Shavitt (1963), Shavitt and Karplus (1965)); population biology and ecological systems (Camacho et al. (2002)).
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8: 5.2 Definitions
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5.2.1
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9: 27.16 Cryptography
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►To do this, let denote the reciprocal of modulo , so that for some integer .
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