Abstract
We discuss the error term in the asymptotic formula for the number of integral points with coprime coordinates in star like plane domains assuming the validity of the Riemann Hypothesis.
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References
Axer, A.: Über einige Grenzwertsätze. Sitzungsber. Kaiserl. Akad. Wiss. Wien. Math.-Naturw. Kl., Bd.120, 1253–1298, Abt. IIa (1911).
Fricker, F.: Einführung in die Gitterpunktlehre. Basel: Birkhäuser. 1982.
Graham, S. W.: The distribution of squarefree numbers J. London Math. Soc.24, 54–64 (1981).
Hardy, G. H., Littlewood, J.E.: Some problems of Diophantine approximation: The lattice points of a right-angled triangle. Proc. London Math. Soc. (2)20, 15–36 (1921); (Second memoir) Abh. Math. Sem. Univ. Hamburg.1, 212–249 (1922).
Hecke, E.: Vorlesungen über die Theorie der algebraischen Zahlen. Leipzig: Akad. Verlagsbuchhandlung. 1923.
Landau, E.: Vorlesungen über Zahlentheorie, Bd. 2. Leipzig: 1927.
Littlewood, J. E.: Quelques consequénces de l'hypothése que la fonction ζ (s) de Riemann n'a pas de zéros dans le demi-plan Res>1/2. C. R. Acad. Sci. (Paris)154, 263–266 (1912).
Montgomery, H. L., Vaughan, R. C.: The distribution of squarefree numbers. In: Recent Progress in Number TheoryHalberstam, H., Hooley, C., eds., pp. 247–256. London: Academic Press. 1981.
Moroz, B. Z.: On the convolution of HeckeL-functions. Mathematika27, 312–320 (1980).
Moroz, B. Z.: Lattice point problems (a few consequences of the Riemann Hypothesis). Preprint. I. H. E. S., M/82/47. 1982.
Neumann, W.D., Zagier, D.: Volumes of hyperbolic three-manifolds. Preprint. University of Maryland. 1983.
Titchmarsh, E. C.: The Theory of the Riemann Zeta-function. Oxford. 1951.
Wu Fang: The lattice points in an ellipse. Chinese Math.4, 260–274 (1963).
Zagier, D. B.: On the number of Markoff numbers below a given boundary. Math. Comp.39, 709–723 (1982).
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Moroz, B.Z. On the number of primitive lattice points in plane domains. Monatshefte für Mathematik 99, 37–42 (1985). https://doi.org/10.1007/BF01300737
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DOI: https://doi.org/10.1007/BF01300737