Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-27T22:15:27.512Z Has data issue: false hasContentIssue false
  • English
  • Français

On the representation of integers with large square factors by positive definite ternary quadratic forms

Published online by Cambridge University Press:  26 February 2010

A. G. Earnest
A. G. Earnest
Affiliation:
Department of Mathematics, Southern Illinois University, Carbondale, Illinois 62901, U.S.A.
Get access

Abstract

It is proved here that, if G is a positive definite integral ternary quadratic lattice of discriminant d and c is a squarefree integer which is primitively represented by the genus of G, then G primitively represents all sufficiently large integers of the type ct2, with g.c.d. (t, 2d) = 1, which are primitively represented by the spinor genus of G.

Type
Research Article
Information
Mathematika , Volume 31 , Issue 2 , December 1984 , pp. 252 - 257
Copyright
Copyright © University College London 1984

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Benham, J. W. and Hsia, J. S.. On spinor exceptional representations. Nagoya Math. J., 87 (1982), 247–260.CrossRefGoogle Scholar
2.Cassels, J. W. S.. Rationale quadratische Formen. Jber. d. Dt. Math.-Verein., 82 (1980, 81–93.Google Scholar
3.Earnest, A. G.. Representation of spinor exceptional integers by ternary quadratic forms. Nagoya Math. J., 93 (1984, 27–38.CrossRefGoogle Scholar
4.Hsia, J. S.. Spinor norms of integral rotations. I. Pacific J. Math., 57 (1975, 199–206.CrossRefGoogle Scholar
5.Jones, B. W.. Quasi-genera of quadratic forms. J. Number Theory, 9 (1977, 393–412.CrossRefGoogle Scholar
6.Jones, B. W.. Exceptional ternary forms and quasi-genera. Preprint.Google Scholar
7.Kitaoka, Y.. Modular forms of degree n and representation by quadratic forms II. Nagoya Math. J., 87 (1982), 127–146.CrossRefGoogle Scholar
8.Malyshev, A. V.. On the representation of integers by positive quadratic forms (Russian). Trudy Mat. Inst. Stekiov, 65 (1962).Google Scholar
9.O'Meara, O. T.. Introduction to Quadratic Forms (Springer, Berlin-Heidelberg-New York, 1963).CrossRefGoogle Scholar
10.Peters, M.. Darstellungen durch definite ternare quadratische Formen. Ada Arith., 34 (1977, 57–80.CrossRefGoogle Scholar
11.Schulze-Pillot, R.. Darstellung durch Spinorgeschlechter ternarer quadratischer Formen. J. Number Theory, 12 (1980, 529–540.CrossRefGoogle Scholar
12.Schulze-Pillot, R.. Thetareihen positiv definiter quadratischer Formen. Invent. Math., 75 (1984, 283–299.CrossRefGoogle Scholar
13.Teterin, Y. G.. On the representation of integers, divisible by a large square, by a positive ternary quadratic form (Russian). Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova, 106 (1981, 135–157.Google Scholar
14.Watson, G. L.. Integral Quadratic Forms (Cambridge University Press, 1960).Google Scholar