Keywords
- Lattice Point
- Planar Domain
- Riemann Hypothesis
- Logarithmic Factor
- Divisor Problem
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
Bombieri, E., and Iwaniec, H.: On the order of ζ(½ + it). Ann.Scuola Norm.Sup. Pisa, Ser. IV, 13, 449–472 (1986).
Cassels, J.W.S.: An introduction to Diophantine approximation. Cambridge: University Press 1957.
Duttlinger, J. and Schwarz, W.: Über die Verteilung der Pythagoräischen Dreiecke. Colloquium Math. 43, 365–372 (1980).
Fricker, F.: Einführung in die Gitterpunktlchre. Basel-Boston-Stuttgart: Birkhäuser 1982.
Hlawka, E.: Theorie der Gleichverteilung. Mannheim-Wien-Zürich: Bibl. Inst. 1979.
Huxley, M.: Exponential sums and lattice points. To appear in Proc. London Math. Soc.
Huxley, M., and Watt, N.: Exponential sums and the Riemann zeta-function. Proc. London Math. Soc. 57, 1–24 (1988).
Iwaniec, H., and Mozzochi, C.J.: On the divisor and circle problems. J. Number Th. 29, 60–93 (1988).
Khintchine, A.: Kettenbrüche. Leipzig: Teubner 1956.
Krätzel, E.: Lattice points. VEB Dt. Verlag d. Wiss.: Berlin 1988.
Krätzel, E.: Mittlere Darstellung natürlicher Zahlen als Differenz zweier k-ter Potenzen. Acta Arith. 16, 111–121 (1969).
Lambek, J. and Moser, L.: On the distribution of Pythagorean triangles. Pacific J. of Math. 5, 73–83 (1955).
Montgomery, H., and Vaughan, R.C.: The distribution of squarefree numbers. In: Recent progress in analytic number theory, Proc. Durham Symp. 1979, vol. I (eds.: H. Halberstam and C. Hooley), pp. 247–256. London: Academic Press 1981.
Moroz, B.Z.: On the number of primitive lattice points in plane domains. Monatsh. Math. 99, 37–42 (1985).
Müller, W., and Nowak, W.G.: On lattice points in planar domains. Math. J. Okayama Univ. 27, 173–184 (1985).
Müller, W., and Nowak, W.G.: Lattice points in domains |x|p + |y|P ≤ R P. Arch. Math. 51, 55–59 (1988).
Müller, W., and Nowak, W.G.: On a mean-value theorem concerning differences of two k-th powers. Tsukuba Math. J. 13, 23–29 (1989).
Müller, W., Nowak, W.G., and Menzer, H.: On the number of primitive pythagorean triangles. Ann.sci.math. Québec 12, 263–273 (1988).
Nowak, W.G.: Zur Gitterpunktlehre der euklidischen Ebene. Indag. Math. 46, 209–213 (1984).
Nowak, W.G.: On a result of Smith and Subbarao concerning a divisor problem. Can.Math.Bull. 27, 501–504 (1984).
Nowak, W.G.: Primitive lattice points in rational ellipses and related arithmetic functions. Monatsh. Math. 106, 57–63 (1988).
Nowak, W.G.: On a divisor problem in arithmetic progressions. J. Number Th. 31, 174–182 (1989).
Nowak, W.G.: On sums of two coprime k-kh powers. Monatsh. Math., to appear.
Phillips, E.: The zeta-function of Riemann; further developments of Van der Corput's method. Quart. J. Oxford 4, 209–225 (1933).
Richert, H.-E.: Über die Anzahl Abelscher Gruppen. I. Math.Z. 56, 21–32 (1952). II. ibid. 58, 71–84 (1953).
Swinnerton-Dyer, H.P.F.: The number of lattice points on a convex curve. J. Number Theory 6, 128–135 (1974).
Titchmarsh, E.C.: The theory of the Riemann zeta function. Oxford: Clarendon Press 1951.
Van der Corput, J.G.: Zahlentheoretische Abschätzungen mit Anwendung auf Gitterpunktprobleme. Math. Z. 17, 250–259 (1923).
Walfisz, A.: Weylsche Exponentialsummen in der neueren Zahlentheorie. Berlin: VEB Dt. Verlag d. Wiss. 1962.
Watt, N.: Exponential sums and the Riemann zeta-function II. Proc. London Math. Soc., to appear.
Wild, R.E.: On the number of primitive Pythagorean triangles with area less than n. Pacific J. of Math. 5, 85–91 (1955).
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© 1990 Springer-Verlag
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Müller, W., Nowak, W.G. (1990). Lattice points in planar domains: Applications of Huxley's ‘discrete hardy-littlewood method’. In: Hlawka, E., Tichy, R.F. (eds) Number-Theoretic Analysis. Lecture Notes in Mathematics, vol 1452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096987
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DOI: https://doi.org/10.1007/BFb0096987
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