Sums of four squares in a quadratic ring
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- by Harvey Cohn and Gordon Pall PDF
- Trans. Amer. Math. Soc. 105 (1962), 536-556 Request permission
References
- Harvey Cohn, Numerical study of the representation of a totally positive quadratic integer as the sum of quadratic integral squares, Numer. Math. 1 (1959), 121–134. MR 107627, DOI 10.1007/BF01386378
- Harvey Cohn, Decomposition into four integral squares in the fields of $2^{1/2}$ and $3^{1/2}$, Amer. J. Math. 82 (1960), 301–322. MR 113855, DOI 10.2307/2372737
- Harvey Cohn, Cusp forms arising from Hilbert’s modular functions for the field of $3^{1/2}$, Amer. J. Math. 84 (1962), 283–305. MR 144884, DOI 10.2307/2372763 L. E. Dickson, History of the theory of numbers, Vol. III, Carnegie Institution, Washington, D. C., 1923, pp. 228-229.
- Jürgen Dzewas, Quadratsummen in reellquadratischen Zahlkörpern, Math. Nachr. 21 (1960), 233–284 (German). MR 112872, DOI 10.1002/mana.19600210309
- Fritz Götzky, Über eine zahlentheoretische Anwendung von Modulfunktionen zweier Veränderlicher, Math. Ann. 100 (1928), no. 1, 411–437 (German). MR 1512493, DOI 10.1007/BF01448854
- L. J. Mordell, On the representation of a binary quadratic form as a sum of squares of linear forms, Math. Z. 35 (1932), no. 1, 1–15. MR 1545284, DOI 10.1007/BF01186544
- Ivan Niven, Integers of quadratic fields as sums of squares, Trans. Amer. Math. Soc. 48 (1940), 405–417. MR 3000, DOI 10.1090/S0002-9947-1940-0003000-5
- Gordon Pall, The structure of the number of representations function in a binary quadratic form, Trans. Amer. Math. Soc. 35 (1933), no. 2, 491–509. MR 1501697, DOI 10.1090/S0002-9947-1933-1501697-8
- Gordon Pall, On the arithmetic of quaternions, Trans. Amer. Math. Soc. 47 (1940), 487–500. MR 2350, DOI 10.1090/S0002-9947-1940-0002350-6
- Gordon Pall, Representation by quadratic forms, Canad. J. Math. 1 (1949), 344–364. MR 34795, DOI 10.4153/cjm-1949-032-9
- Gordon Pall, Sums of two squares in a quadratic field, Duke Math. J. 18 (1951), 399–409. MR 40337
- G. Pall and O. Taussky, Application of quaternions to the representations of a binary quadratic form as a sum of four squares, Proc. Roy. Irish Acad. Sect. A 58 (1957), 23–28. MR 0092809 C. L. Siegel, Lectures on the analytical theory of quadratic forms, Mimeographed notes, Princeton, 1935.
Additional Information
- © Copyright 1962 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 105 (1962), 536-556
- MSC: Primary 10.46
- DOI: https://doi.org/10.1090/S0002-9947-1962-0142522-8
- MathSciNet review: 0142522