On a form of the Erdős-Turán inequality

• Autorzy: Jeffrey J. Holt
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1996
• Tom: 74
• Numer: 1
• Strony: 61-66

Daty

wydano

1996

otrzymano

1994-11-02

Twórcy

autor

Jeffrey J. Holt

• Department of Mathematics, Michigan Technological University, Houghton, Michigan 49931, U.S.A.

Bibliografia

• [1] R. C. Baker, Diophantine Inequalities, Oxford University Press, New York, 1986.
• [2] J. Beck and W. W. L. Chen, Irregularities of Distribution, Cambridge University 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] P. J. Grabner, Erdős-Turán type discrepancy bounds, Monatsh. Math. 111 (1991), 127-135.
• [6] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford University Press, Oxford, 1979.
• [7] J. J. Holt and J. D. Vaaler, The Beurling-Selberg extremal functions for a ball in Euclidean space, to appear.
• [8] L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Wiley, New York, 1974.
• [9] W. M. Schmidt, Irregularities of distribution, IV, Invent. Math. 7 (1969), 55-82.
• [10] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, N.J., 1971.
• [11] P. Szüsz, Über ein Problem der Gleichverteilung, in: Comptes Rendus du Premier Congrès des Mathématiciens Hongrois, 1950, 461-472.
• [12] J. D. Vaaler, Some extremal functions in Fourier analysis, Bull. Amer. Math. Soc. 12 (1985), 183-216.
• [13] J. D. Vaaler, Refinements of the Erdős-Turán inequality, in: Number Theory with an Emphasis on the Markoff Spectrum, W. Moran and A. Pollington (eds.), Marcel Dekker, New York, 1993, 263-269