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Proceedings of the American Mathematical Society

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Isolation theorem for products of linear forms


Author: T. W. Cusick
Journal: Proc. Amer. Math. Soc. 100 (1987), 29-33
MSC: Primary 11H46
MathSciNet review: 883396
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Abstract: A theorem of Cassels and Swinnerton-Dyer about products of three linear forms with real coefficients is generalized to products of any number of linear forms.


References [Enhancements On Off] (What's this?)

  • [1] J. W. S. Cassels, An introduction to Diophantine approximation, Cambridge Tracts in Mathematics and Mathematical Physics, No. 45, Cambridge University Press, New York, 1957. MR 0087708
  • [2] -, An introduction to the geometry of numbers, Springer-Verlag, Berlin, 1959.
  • [3] J. W. S. Cassels and H. P. F. Swinnerton-Dyer, On the product of three homogeneous linear forms and the indefinite ternary quadratic forms, Philos. Trans. Roy. Soc. London. Ser. A. 248 (1955), 73–96. MR 0070653
  • [4] B. F. Skubenko, The product of 𝑛 linear forms in 𝑛 variables, Trudy Mat. Inst. Steklov. 158 (1981), 175–179, 230 (Russian). Analytic number theory, mathematical analysis and their applications. MR 662844
  • [5] B. F. Skubenko, Isolation theorem for decomposable forms of totally real algebraic number fields of degree 𝑛≥3, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 112 (1981), 167–171, 202 (Russian). Analytic number theory and the theory of functions, 4. MR 644002

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0883396-X
Keywords: Linear forms, norm forms
Article copyright: © Copyright 1987 American Mathematical Society