Rational approximation to algebraic numbers of small height : the Diophantine equation j axn ÿ byn j

  title={Rational approximation to algebraic numbers of small height : the Diophantine equation j axn {\"y} byn j},
  author={M. A. Bennett}
Following an approach originally due to Mahler and sharpened by Chudnovsky, we develop an explicit version of the multi-dimensional ``hypergeometric method'' for rational and algebraic approximation to algebraic numbers. Consequently, if a; b and n are given positive integers with nZ 3, we show that the equation of the title possesses at most one solution in positive integers x; y. Further results on Diophantine equations are also presented. The proofs are based upon explicit Pade… CONTINUE READING
Highly Cited
This paper has 21 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.


Publications referenced by this paper.
Showing 1-10 of 33 references

Springer Verlag

Th. Schneider, EinfuÈhrung in die transzendenten Zahlen
Berlin-GoÈttingen-Heidelberg • 1957
View 4 Excerpts
Highly Influenced


A. O. Gelfond, Transcendental, Algebraic Numbers, F Englishtransl.byL.
Dover Publications Inc., New York • 1960
View 3 Excerpts
Highly Influenced

The equation …xn ÿ 1†=…xÿ 1† ˆ y with x square, Math

N. Saradha, T. N. Shorey
Proc. Cambridge Philos. Soc • 1999

Explicit Lower Bounds for Rational Approximation to

AlgebraicNumbersMICHAEL A. BENNETTAbstractIn

̈ective measures of irrationality for certain algebraic numbers

E M. Bennett
J. Austral. Math. Soc • 1997

Perfect powers in products of integers from a block of consecutive integers (II)

Y. Nesterenko, T. N. Shorey
Acta Arith • 1996

Similar Papers

Loading similar papers…