# Asymptotic aspects of the Diophantine equation ${p}^{k}{x}^{nk}-{z}^{k}=l$

Acta Arithmetica (2000)

- Volume: 92, Issue: 2, page 131-140
- ISSN: 0065-1036

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top## How to cite

topWolfgang Jenkner. "Asymptotic aspects of the Diophantine equation $p^{k}x^{nk} - z^{k} = l$." Acta Arithmetica 92.2 (2000): 131-140. <http://eudml.org/doc/207375>.

@article{WolfgangJenkner2000,

author = {Wolfgang Jenkner},

journal = {Acta Arithmetica},

keywords = {higher degree Diophantine equations; asymptotic results; lattice points},

language = {eng},

number = {2},

pages = {131-140},

title = {Asymptotic aspects of the Diophantine equation $p^\{k\}x^\{nk\} - z^\{k\} = l$},

url = {http://eudml.org/doc/207375},

volume = {92},

year = {2000},

}

TY - JOUR

AU - Wolfgang Jenkner

TI - Asymptotic aspects of the Diophantine equation $p^{k}x^{nk} - z^{k} = l$

JO - Acta Arithmetica

PY - 2000

VL - 92

IS - 2

SP - 131

EP - 140

LA - eng

KW - higher degree Diophantine equations; asymptotic results; lattice points

UR - http://eudml.org/doc/207375

ER -

## References

top- [1] D. Clark, An arithmetical function associated with the rank of elliptic curves, Canad. Math. Bull. 34 (1991), 181-185. Zbl0695.14014
- [2] A. Erdélyi, Asymptotic Expansions, Dover, New York, 1956. Zbl0070.29002
- [3] M. N. Huxley, Area, Lattice Points and Exponential Sums, Clarendon Press, Oxford, 1996.
- [4] W. Jenkner, On divisors whose sum is a square, Acta Arith. 90 (1999), 113-120. Zbl0933.11009
- [5] E. Krätzel, Lattice Points, Kluwer, Dordrecht, 1988.
- [6] E. Krätzel, Mittlere Darstellungen natürlicher Zahlen als Differenz zweier k-ter Potenzen, Acta Arith. 16 (1969), 111-121. Zbl0201.05003
- [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. Zbl0735.11047
- [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. Zbl0687.10033

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