Asymptotic aspects of the Diophantine equation pkxnk-zk=l
Wolfgang Jenkner
Acta Arithmetica, Tome 92 (2000), p. 131-140 / Harvested from The Polish Digital Mathematics Library
Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:207375
@article{bwmeta1.element.bwnjournal-article-aav92i2p131bwm,
     author = {Wolfgang Jenkner},
     title = {Asymptotic aspects of the Diophantine equation $p^{k}x^{nk} - z^{k} = l$
            },
     journal = {Acta Arithmetica},
     volume = {92},
     year = {2000},
     pages = {131-140},
     zbl = {0999.11056},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav92i2p131bwm}
}
Wolfgang Jenkner. Asymptotic aspects of the Diophantine equation $p^{k}x^{nk} - z^{k} = l$
            . Acta Arithmetica, Tome 92 (2000) pp. 131-140. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav92i2p131bwm/

[000] [1] D. Clark, An arithmetical function associated with the rank of elliptic curves, Canad. Math. Bull. 34 (1991), 181-185. | Zbl 0695.14014

[001] [2] A. Erdélyi, Asymptotic Expansions, Dover, New York, 1956. | Zbl 0070.29002

[002] [3] M. N. Huxley, Area, Lattice Points and Exponential Sums, Clarendon Press, Oxford, 1996.

[003] [4] W. Jenkner, On divisors whose sum is a square, Acta Arith. 90 (1999), 113-120. | Zbl 0933.11009

[004] [5] E. Krätzel, Lattice Points, Kluwer, Dordrecht, 1988.

[005] [6] E. Krätzel, Mittlere Darstellungen natürlicher Zahlen als Differenz zweier k-ter Potenzen, Acta Arith. 16 (1969), 111-121. | Zbl 0201.05003

[006] [7] G. Kuba, A mean value theorem on differences of two k-th powers of numbers in residue classes, Manuscripta Math. 72 (1991), 213-222. | Zbl 0735.11047

[007] [8] W. Müller and W. G. Nowak, On a mean-value theorem concerning differences of two k-th powers, Tsukuba J. Math. 13 (1989), 23-29. | Zbl 0687.10033