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

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D. Clark, An arithmetical function associated with the rank of elliptic curves, Canad. Math. Bull. 34 (1991), 181-185.
A. Erdélyi, Asymptotic Expansions, Dover, New York, 1956.
M. N. Huxley, Area, Lattice Points and Exponential Sums, Clarendon Press, Oxford, 1996.
W. Jenkner, On divisors whose sum is a square, Acta Arith. 90 (1999), 113-120.
E. Krätzel, Lattice Points, Kluwer, Dordrecht, 1988.
E. Krätzel, Mittlere Darstellungen natürlicher Zahlen als Differenz zweier k-ter Potenzen, Acta Arith. 16 (1969), 111-121.
G. Kuba, A mean value theorem on differences of two k-th powers of numbers in residue classes, Manuscripta Math. 72 (1991), 213-222.
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.