Asymptotic aspects of the Diophantine equation p k x n k - z k = l

Wolfgang Jenkner

Acta Arithmetica (2000)

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

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Wolfgang 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

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  1. [1] D. Clark, An arithmetical function associated with the rank of elliptic curves, Canad. Math. Bull. 34 (1991), 181-185. Zbl0695.14014
  2. [2] A. Erdélyi, Asymptotic Expansions, Dover, New York, 1956. Zbl0070.29002
  3. [3] M. N. Huxley, Area, Lattice Points and Exponential Sums, Clarendon Press, Oxford, 1996. 
  4. [4] W. Jenkner, On divisors whose sum is a square, Acta Arith. 90 (1999), 113-120. Zbl0933.11009
  5. [5] E. Krätzel, Lattice Points, Kluwer, Dordrecht, 1988. 
  6. [6] E. Krätzel, Mittlere Darstellungen natürlicher Zahlen als Differenz zweier k-ter Potenzen, Acta Arith. 16 (1969), 111-121. Zbl0201.05003
  7. [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. [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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