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.

**[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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DOI:
https://doi.org/10.1090/S0002-9939-1987-0883396-X

Keywords:
Linear forms,
norm forms

Article copyright:
© Copyright 1987
American Mathematical Society