The application of the Shimura lifting to the representation of large numbers of ternary quadratic forms
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Abstract
One obtains an asymptotic formula for the number of the representations of numbers, divisible by a large square, by a positive ternary integral quadratic form. One gives an estimate of the remainder, unimprovable with respect to the quadratic part and uniform with respect to the square-free part of the represented number.
Keywords
Quadratic Form Asymptotic Formula Quadratic Part Integral Quadratic Form Ternary Quadratic Form
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Literature cited
- 1.Yu. V. Linnik, “A general theorem on the representation of numbers by separate ternary quadratic forms,” Izv. Akad. Nauk SSSR, Ser. Mat.,3, No. 1, 87–108 (1939).Google Scholar
- 2.A. V. Malyshev, “Representation of integers by positive quadratic forms,” Trudy Mat. Inst. Akad. Nauk SSSR,65 (1962).Google Scholar
- 3.Yu. G. Teterin, “On the representation of numbers, divisible by a large square, by a positive ternary quadratic form,” J. Sov. Math.,23, No. 2 (1983).Google Scholar
- 4.A. N. Andrianov, “On the analytic arithmetic of quadratic forms in an odd number of variables in connection with the theory of modular forms,” Dokl. Akad. Nauk SSSR,145, No. 2, 241–244 (1962).Google Scholar
- 5.G. Shimura, “On modular forms of half integral weight,” Ann. Math.,97, No. 3, 440–481 (1973).Google Scholar
- 6.S. Niwa, “Modular forms of half integral weight and the integral of certain theta-functions,” Nagoya Math. J.,56, 147–161 (1975).Google Scholar
- 7.Y. Z. Flicker, “Automorphic forms on covering groups of GL(2),” Invent. Math.,57, No. 2, 119–182 (1980).Google Scholar
- 8.G. Shimura, “The critical values of certain zeta functions associated with modular forms of half-integral weight,” J. Math. Soc. Jpn.,33, No. 4, 649–672 (1981).Google Scholar
- 9.J.-L. Waldspurger, “Sur les coefficients de Fourier des formes modulaires de poids demientier,” J. Math. Pures Appl.,60, No. 4, 375–484 (1981).Google Scholar
- 10.E. P. Golubeva and O. M. Fomenko, “The values of Dirichlet series, associated with modular forms, at the points s=1/2, 1,” J. Sov Math.,36, No. 1 (1987).Google Scholar
- 11.R. Schulze-Pillot, “Thetareihen positiv definiter quadratischer Formen,” Invent. Math.,75, No. 2, 283–299 (1984).Google Scholar
- 12.B. W. Jones and G. Pall, “Regular and semiregular positive ternary quadratic forms,” Acta Math.,70, 165–191 (1939).Google Scholar
- 13.G. A. Lomadze, “Formulas for the number of representations of numbers by certain regular and semiregular ternary quadratic forms belonging to two-class genera,” Acta Arith.,34, No. 2, 131–162 (1978).Google Scholar
- 14.M. Peters, “Darstellungen durch definite ternare quadratische Formen,” Acta Arith.,34, No. 1, 57–80 (1977).Google Scholar
- 15.Yu. G. Teterin, “The representation of numbers by spinor genera,” Preprint LOMI, R-2-84, Leningrad (1984).Google Scholar
- 16.E. P. Golubeva and O. M. Fomenko, The appliation of spherical function to a certain problem in the theory of quadratic forms,” J. Sov. Math. (this issue).Google Scholar
- 17.B. A. Cipra, “On the Niwa-Shintani theta-kernel lifting of modular forms,” Nagoya Math. J.,91, 49–117 (1983).Google Scholar
- 18.M.-F. Vigneras, “Facteurs gamma et équations fonctionnelles,” Lect. Notes Math., No. 627, 79–103 (1977).Google Scholar
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© Plenum Publishing Corporation 1987