Diophantine approximation of ternary linear forms. II

Author:
T. W. Cusick

Journal:
Math. Comp. **26** (1972), 977-993

MSC:
Primary 10F15

MathSciNet review:
0321879

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Abstract: Let denote the positive root of the equation ; that is, . The main result of the paper is the evaluation of the constant , where the min is taken over all integers satisfying . Its value is . The same method can be applied to other constants of the same type.

**[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]**T. W. Cusick,*Diophantine approximation of ternary linear forms*, Math. Comp.**25**(1971), 163–180. MR**0296022**, 10.1090/S0025-5718-1971-0296022-4**[3]**H. Davenport and Wolfgang M. Schmidt,*Dirichlet’s theorem on diophantine approximation*, Symposia Mathematica, Vol. IV (INDAM, Rome, 1968/69) Academic Press, London, 1970, pp. 113–132. MR**0272722****[4]**H. Davenport and W. M. Schmidt,*Dirichlet’s theorem on diophantine approximation. II*, Acta Arith.**16**(1969/1970), 413–424. MR**0279040****[5]**V. Jarnik, ``Problem 278,''*Colloq. Math.*, v. 6, 1958, pp. 337-338.**[6]**J. Lesca,*Thesis*, University of Grenoble, France, 1968.

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DOI:
https://doi.org/10.1090/S0025-5718-1972-0321879-9

Keywords:
Ternary linear forms,
Dirichlet's Diophantine approximation theorem,
totally real cubic field

Article copyright:
© Copyright 1972
American Mathematical Society