Abstract
One obtains theoretic-numerical results connected with the investigation of the Fourier coefficients of theta-series, associated with indefinite ternary quadratic forms.
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Literature cited
C. L. Siegel, “Indefinite quadratische Formen und Funktionentheorie. I,” Math. Ann.,124, No. 1, 17–54 (1951).
H. Maass, “Über die räumliche Verteilung der Punkte in Gittern mit indefiniter Metrik,” Math. Ann.,138, No. 4, 287–315 (1959).
K. G. Ramanathan, “On the analytic theory of quadratic forms,” Acta Arith.,21, 423–436 (1972).
C. L. Siegel, “Über die analytische Theorie der quadratischen Forman. I–III,” Ann. Math.,36, 527–606 (1935);37, 230–263 (1936);313, 212–291 (1937).
R. Fricke and F. Klein, Vorlesungen über die Theorie der Automorphen Funktionen, Band I, Teubner, Leipzig (1926).
H. Huber, “Über eine neue Klass automorpher Funktionen und Ein Gitterpunktproblem in der hyperbolischen Ebene. I,” Comment. Math. Helv.,30, No. 1, 20–62 (1956).
B. W. Jones, The Arithmetic Theory of Quadratic Forms, Baltimore (1950).
T. Shintani, “On zeta-functions associated with the vector space of quadratic forms,” J. Fac. Sci. Univ. Tokoyo Sect. IA Math.,22, No. 1, 25–65 (1975).
E. P. Golubeva and O. M. Fomenko, “The distribution of integral points on two-sheeted hyperboloids,” Tr. Mat. Inst. Akad. Nauk SSSR,158, 69–79 (1981).
A. I. Vinogradov and L. A. Takhtadzhyan, “On the Linnik-Skubenko asymptotics,” Dokl. Akad. Nauk SSSR,253, No. 4, 777–780 (1980).
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 112, pp. 41–50, 1981.
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Golubeva, E.P., Fomenko, O.M. Theta-series associated with indefinite ternary quadratic forms and the related Dirichlet series. J Math Sci 25, 999–1006 (1984). https://doi.org/10.1007/BF01680822
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DOI: https://doi.org/10.1007/BF01680822