Explicit estimates of solutions of some Diophantine equations

Juricevic, Robert

Funct. Approx. Comment. Math., Tome 38 (2008) no. 1, p. 171-194 / Harvested from Project Euclid

Résumé

Let $k$ be a fixed non-zero integer, and let $x$ and $y$ be integers such that $$y^2=x^3+k.$$ We show that $$\log \max\{|x|,|y|\}<\min_{(c,d)\in S} \{c|k|(\log |k|)^d\},$$ where $$S=\{(10^{181},4), (10^{23},5), (10^{19},6)\}.$$

Publié le : 2008-09-15
Classification: Mordell equation, Hall's conjecture, linear forms in logarithms, 11D25, 11J86, 11D99

@article{1229696538,
     author = {Juricevic, Robert},
     title = {Explicit estimates of solutions of some Diophantine equations},
     journal = {Funct. Approx. Comment. Math.},
     volume = {38},
     number = {1},
     year = {2008},
     pages = { 171-194},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1229696538}
}

Juricevic, Robert. Explicit estimates of solutions of some Diophantine equations. Funct. Approx. Comment. Math., Tome 38 (2008) no. 1, pp.  171-194. http://gdmltest.u-ga.fr/item/1229696538/