Diophantine approximation of ternary linear forms. II

Author:
T. W. Cusick

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

MSC:
Primary 10F15

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

MathSciNet review:
0321879

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Abstract | References | Similar Articles | Additional Information

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 Math. and Math. Phys., no. 45, Cambridge Univ. Press, New York, 1957. MR**19**, 396. MR**0087708 (19:396h)****[2]**T. W. Cusick, ``Diophantine approximation of ternary linear forms,''*Math. Comp.*, v. 25, 1971, pp. 163-180. MR**0296022 (45:5083)****[3]**H. Davenport & W. M. Schmidt, ``Dirichlet's theorem on diophantine approximation,''*Symposia Mathematica*. Vol. IV (INDAM, Rome, 1968/69), Academic Press, London, 1970, pp. 113-132. MR**42**#7603. MR**0272722 (42:7603)****[4]**H. Davenport & W. M. Schmidt, ``Dirichlet's theorem on Diophantine approximation. II,''*Acta Arith.*, v. 16, 1969/70, pp. 413-424. MR**0279040 (43:4766)****[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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Additional Information

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