Abstract
One obtains results related with the representation of integers as sums of three squares in imaginary quadratic fields.
Similar content being viewed by others
Literature cited
H. Cohn and G. Pall, “Sums of four squares in a quadratic ring,” Trans. Am. Math. Soc.,105, No. 3, 536–556 (1962).
M. Peters, “Summen von Quadraten in Zahlringer,” J. Reine Angew. Math.,268/269, 318–323 (1974).
D. R. Estes and J. S. Hsia, “Exceptional integers of some ternary quadratic forms,” Adv. Math.,45, No. 3, 310–318 (1982).
G. Pall and O. Taussky, “Application of quaternions to the representation of a binary quadratic form as a sum of four squares,” Proc. R. Irish Acad.,58, Sec. A, No. 3, 23–28 (1957).
O. M. Fomenko, “On certain Diophantine systems,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,116, 155–160 (1982).
T. Estermann, “An asymptotic formula in the theory of numbers,” Proc. London Math. Soc.,34, 280–292 (1932).
G. Pall, “Quaternions and sums of three squares,” Am. J. Math.,64, No. 3; 503–513 (1942).
G. Pall, “Representation by quadratic forms,” Can. J. Math.,1, No. 4, 344–364 (1949).
A. Selberg, “On the estimation of Fourier coefficients of modular forms,” in: Proc. Sympos. Pure. Math., Vol. 8, Number Theory, Amer. Math. Soc., Providence (1965), pp. 1–15.
N. V. Kuznetosv, “Spectral methods in arithmetic problems,” Zap. Nauchn. Sem. Leningr., Otd. Mat. Inst.,76, 159–166 (1978).
V. A. Bykovskii, “On a certain summation formula in the spectral theory of automorphic functions and its application to analytic number theory,” Dokl. Akad. Nauk SSSR,264, No. 2, 275–277 (1982).
J.-M. Deshouillers and H. Iwaniec, “An additive divisor problem,” J. London Math. Soc.,26, No. 1, 1–14 (1982).
J. W. Porter, “On a theorem of Heilbronn,” Mathematika,22, No. 1, 20–28 (1975).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 125, pp. 184–197, 1983.
Rights and permissions
About this article
Cite this article
Fomenko, O.M. Sum of squares in imaginary quadratic fields. J Math Sci 26, 2424–2432 (1984). https://doi.org/10.1007/BF01680024
Issue Date:
DOI: https://doi.org/10.1007/BF01680024