An effective lower bound for the height of algebraic numbers
Primitive divisors of certain elliptic divisibility sequences
Lang's conjecture and sharp height estimates for the elliptic curves y² = x³ + b
For , we establish Lang’s conjecture on a lower bound for the canonical height of nontorsion points along with upper and lower bounds for the difference between the canonical and logarithmic heights. These results are either best possible or within a small constant of the best possible lower bounds.
On the Number of S-Integral Solutions to Ym = f(x).
Primitive divisors of Lucas and Lehmer sequences, II
Let and are conjugate complex algebraic integers which generate Lucas or Lehmer sequences. We present an algorithm to search for elements of such sequences which have no primitive divisors. We use this algorithm to prove that for all and with h, the -th element of these sequences has a primitive divisor for . In the course of proving this result, we give an improvement of a result of Stewart concerning more general sequences.
Thue's Fundamentaltheorem, I: The general case
Effective irrationality measures and approximation by algebraic conjugates
Rational approximations to and other algebraic numbers revisited
In this paper, we establish improved effective irrationality measures for certain numbers of the form , using approximations obtained from hypergeometric functions. These results are very close to the best possible using this method. We are able to obtain these results by determining very precise arithmetic information about the denominators of the coefficients of these hypergeometric functions. Improved bounds for the Chebyshev functions in arithmetic progressions and for are...
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