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Biquadratic reciprocity laws


Author: Ezra Brown
Journal: Proc. Amer. Math. Soc. 37 (1973), 374-376
MSC: Primary 10A15
DOI: https://doi.org/10.1090/S0002-9939-1973-0313172-8
MathSciNet review: 0313172
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Abstract: Let $ p \equiv q \equiv 1\;(\bmod 4)$ be distinct primes such that $ (p\vert q) = 1$, and let $ g = [k,2m,n]$ be a binary quadratic form of determinant q which represents p. Subject to certain restrictions on k and q, we obtain some reciprocity laws for the fourth-power residue symbols $ {(p\vert q)_4}$ and $ {(q\vert p)_4}$.


References [Enhancements On Off] (What's this?)

  • [1] Ezra Brown, A theorem on biquadratic reciprocity, Proc. Amer. Math. Soc. 30 (1971), 220-222. MR 43 #6182. MR 0280462 (43:6182)
  • [2] -, Quadratic forms and biquadratic reciprocity, J. Reine Angew. Math. 253 (1972), 214-220. MR 0296019 (45:5080)
  • [3] Klaus Burde, Ein rationales biquadratisches Reziprozitätsgesetz, J. Reine Angew. Math. 235 (1969), 175-184. MR 39 #2694. MR 0241354 (39:2694)
  • [4] Martin Kneser, Klassenzahlen indefiniter quadratischer Formen in drei oder mehr Veränderlichen, Arch. Math. 7 (1956), 323-332. MR 18, 562. MR 0082514 (18:562f)
  • [5] Emma Lehmer, Some special quartic reciprocity laws (to appear). MR 0302603 (46:1747)
  • [6] Gordon Pall, On generalized quaternions, Trans. Amer. Math. Soc. 59 (1946), 280-332. MR 8, 318. MR 0018702 (8:318b)
  • [7] A. Scholz, Über die Lösbarkeit der Gleichung $ {t^2} - D{u^2} = - 4$, Math. Z. 39 (1935), 95-111. MR 1545490

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DOI: https://doi.org/10.1090/S0002-9939-1973-0313172-8
Article copyright: © Copyright 1973 American Mathematical Society

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