Rational Approximation to Algebraic Numbers of Small Height
نویسنده
چکیده
Following an approach originally due to Mahler and sharpened by Chudnovsky, we develop an explicit version of the multi-dimensional \hy-pergeometric method" for rational and algebraic approximation to algebraic numbers. Consequently, if a; b and n are given positive integers with n 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 Pad e approximations to systems of bi-nomial functions, together with new Chebyshev-like estimates for primes in arithmetic progressions and a variety of computational techniques.
منابع مشابه
Approximation to Real Numbers by Cubic Algebraic Integers I
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