On successive applications of two new p-adic estimates for linear forms in the log-arithms of algebraic numbers due to Yu and an earlier Archimedean estimate for linear forms in the logarithms of algebraic numbers due to Baker and Wüstholz, Stewart and Yu have recently succeeded in proving that there exists an effectively computable absolute constant c such that for all positive integers x, y and z satis-fying x + y = z, (x,y,z) = 1, and z > 2,
log z < G1/3+c/ log log G,
where G is the greatest square-free factor of xyz.
In this paper, we will prove that the constant c can be bounded from above by 15, whence furnishing an explicit result related to the abc-conjecture.
Permanent URL for this record: https://lbezone.hkust.edu.hk/bib/b645947