Diophantine approximation of ternary linear forms

Author:
T. W. Cusick

Journal:
Math. Comp. **25** (1971), 163-180

MSC:
Primary 10F99

DOI:
https://doi.org/10.1090/S0025-5718-1971-0296022-4

MathSciNet review:
0296022

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The paper gives an efficient method for finding arbitrarily many solutions in integers *x, y, z* of the Diophantine inequality , where defines a totally real cubic field *F* over the rationals, the numbers 1, form an integral basis for *F*, and *c* is a constant which can be calculated in terms of parameters of the method. For certain values of *c*, the method generates all solutions of the inequality.

**[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]**H. Hancock,*Development of the Minkowski Geometry of Numbers*, Macmillan, New York, 1939, pp. 371-452. MR**1**, 67.**[3]**H. Minkowski, "Zur Theorie der Kettenbrüche," in*Gesammelte Abhandlungen*. Vol. I, Teubner, Leipzig, 1911, pp. 278-292.**[4]**L. G. Peck,*Simultaneous rational approximations to algebraic numbers*, Bull. Amer. Math. Soc.**67**(1961), 197–201. MR**0122772**, https://doi.org/10.1090/S0002-9904-1961-10565-X**[5]**M. Zeisel, "Zur Minkowskischen Parallelepipedapproximation,"*S.-B. Akad. Wiss. Wien*, v. 126, 1917, pp. 1221-1247.

Retrieve articles in *Mathematics of Computation*
with MSC:
10F99

Retrieve articles in all journals with MSC: 10F99

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1971-0296022-4

Keywords:
Diophantine inequality,
ternary linear forms,
totally real cubic field

Article copyright:
© Copyright 1971
American Mathematical Society