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

• Autorzy: Wolfgang Jenkner
• Języki publikacji: EN

Kategorie tematyczne

• 11D25: Cubic and quartic equations
• 11N37: Asymptotic results on arithmetic functions
• 11N25: Distribution of integers with specified multiplicative constraints
• 11D41: Higher degree equations; Fermat's equation
• 11G30: Curves of arbitrary genus or genus ≠ 1 over global fields
• 11G05: Elliptic curves over global fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2000
• Tom: 92
• Numer: 2
• Strony: 131-140

Daty

wydano

2000

otrzymano

1998-05-22

poprawiono

1999-07-14

Twórcy

autor

Wolfgang Jenkner

• Institut für Mathematik, Universität Wien, Strudlhofgasse 4, 1090 Wien, Austria

Bibliografia

• [1] D. Clark, An arithmetical function associated with the rank of elliptic curves, Canad. Math. Bull. 34 (1991), 181-185.
• [2] A. Erdélyi, Asymptotic Expansions, Dover, New York, 1956.
• [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.
• [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.
• [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.
• [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.