Diophantine approximation of ternary linear forms. II
Author:
T. W. Cusick
Journal:
Math. Comp. 26 (1972), 977993
MSC:
Primary 10F15
MathSciNet review:
0321879
Fulltext PDF Free Access
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 Mathematics and Mathematical Physics, No. 45, Cambridge
University Press, New York, 1957. MR 0087708
(19,396h)
 [2]
T.
W. Cusick, Diophantine approximation of ternary
linear forms, Math. Comp. 25 (1971), 163–180. MR 0296022
(45 #5083), http://dx.doi.org/10.1090/S00255718197102960224
 [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
(42 #7603)
 [4]
H.
Davenport and W.
M. Schmidt, Dirichlet’s theorem on diophantine approximation.
II, Acta Arith. 16 (1969/1970), 413–424. MR 0279040
(43 #4766)
 [5]
V. Jarnik, ``Problem 278,'' Colloq. Math., v. 6, 1958, pp. 337338.
 [6]
J. Lesca, Thesis, University of Grenoble, France, 1968.
 [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. 163180. 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. 113132. 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. 413424. MR 0279040 (43:4766)
 [5]
 V. Jarnik, ``Problem 278,'' Colloq. Math., v. 6, 1958, pp. 337338.
 [6]
 J. Lesca, Thesis, University of Grenoble, France, 1968.
Similar Articles
Retrieve articles in Mathematics of Computation
with MSC:
10F15
Retrieve articles in all journals
with MSC:
10F15
Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197203218799
PII:
S 00255718(1972)03218799
Keywords:
Ternary linear forms,
Dirichlet's Diophantine approximation theorem,
totally real cubic field
Article copyright:
© Copyright 1972
American Mathematical Society
