Representation of numbers by quadratic forms in algebraic number fields. (English. Russian original) Zbl 0663.10018
J. Sov. Math. 43, No. 5, 2663-2669 (1988); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 151, 68-77 (1986).
See the review in Zbl 0596.10021.
MSC:
| 11E12 | Quadratic forms over global rings and fields |
| 11E41 | Class numbers of quadratic and Hermitian forms |
| 11P55 | Applications of the Hardy-Littlewood method |
| 11E16 | General binary quadratic forms |
Keywords:
representations of integers; totally real field; totally positive definite quadratic form; singular integral; singular series; finitely many primitive classes; quadratic forms of type PReferences:
| [1] | A. B. Voronetskii and E. A. Kashina, ”Sums of squares in algebraic number fields,” in: Topology and Set Theory [in Russian], Izhevsk (1982), pp. 103–110. |
| [2] | E. Hecke, Lectures in Algebraic Number Theory [Russian translation], GITTL, Moscow-Leningrad (1940). |
| [3] | G. P. Gogishvili, ”On finiteness of the number of certain classes of positive primitive quadratic forms,” Trudy TMI im. Razmadze,45, 778–1100 (1974). |
| [4] | L. A. Kogan, B. T. Tashpulatov, and S. R. Faiziev, Representation of Numbers by Quadratic Forms [in Russian], Tashkent (1980). |
| [5] | A. V. Malyshev, ”On representation of integers by positive quadratic forms,” Trudy Mat. Inst. AN SSSR, 65 (1962). |
| [6] | J. Dzewas, ”Quadratsummen in reel-quadratischen Zahlkörpern,” Math. Nachr.,21, 233–284 (1960). · Zbl 0098.03502 · doi:10.1002/mana.19600210309 |
| [7] | W. Narkiewicz, Elementary and Analytic Theory of Algebraic Numbers, Warsaw (1974). · Zbl 0276.12002 |
| [8] | O. T. O’Meara, Introduction to Quadratic Forms (1963). |
| [9] | H. Pfeuffer, ”On the conjecture about class numbers of totally positive quadratic forms in totally real algebraic number fields,” J. Number Theory,11, No. 2, 188–196 (1979). · Zbl 0408.10013 · doi:10.1016/0022-314X(79)90038-6 |
| [10] | R. A. Rankin, ”Sums of squares and cusp forms,” Am. J. Math.,87, No. 4, 857–860 (1965). · Zbl 0132.30802 · doi:10.2307/2373249 |
| [11] | C. L. Siegel, ”Additive Theorie del Zahlkörper. II,” Math. Ann.,88, 184–210 (1923). · JFM 49.0128.01 · doi:10.1007/BF01579178 |
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