On the Erdős-Turán inequality for balls

• Autorzy: Glyn Harman
• Języki publikacji: EN

Kategorie tematyczne

• 11K38: Irregularities of distribution, discrepancy

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1998
• Tom: 85
• Numer: 4
• Strony: 389-396

Daty

wydano

1998

otrzymano

1997-12-15

Twórcy

autor

Glyn Harman

• School of Mathematics, Cardiff University, P.O. Box 926, Cardiff CF2 4YH, Wales, U.K.

Bibliografia

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• [2] J. Beck and W. W. L. Chen, Irregularities of Distribution, Cambridge Univ. Press, 1987.
• [3] T. Cochrane, Trigonometric approximation and uniform distribution modulo 1, Proc. Amer. Math. Soc. 103 (1988), 695-702.
• [4] P. Erdős and P. Turán, On a problem in the theory of uniform distribution, I, Indag. Math. 10 (1948), 370-378.
• [5] G. Harman, Small fractional parts of additive forms, Philos. Trans. Roy. Soc. London Ser. A 345 (1993), 339-347.
• [6] G. Harman, Metric Number Theory, Oxford Univ. Press, 1998.
• [7] J. J. Holt, On a form of the Erdős-Turán inequality, Acta Arith. 74 (1996), 61-66.
• [8] J. J. Holt and J. D. Vaaler, The Beurling-Selberg extremal functions for a ball in Euclidean space, Duke Math. J. 83 (1996), 203-248.
• [9] J. F. Koksma, Some theorems on Diophantine inequalities, Math. Centrum Amsterdam Scriptum no. 5.
• [10] H. L. Montgomery, Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis, Amer. Math. Soc., Providence, R.I., 1994.
• [11] W. M. Schmidt, Metrical theorems on fractional parts of sequences, Trans. Amer. Math. Soc. 110 (1964), 493-518.
• [12] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, N.J., 1971.
• [13] P. Szüsz, Über ein Problem der Gleichverteilung, in: Comptes Rendus du Premier Congrès des Mathématiciens Hongrois, 1950, 461-472.
• [14] S. K. Zaremba, Good lattice points in the sense of Hlawka and Monte Carlo integration, Monatsh. Math. 72 (1968), 264-269.