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On the Distribution of αp Modulo One

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Number Theoretic Methods

Part of the book series: Developments in Mathematics ((DEVM,volume 8))

Abstract

In this article, some topics on the approximation to the real number by rational numbers are introduced. In particular, the author introduces the progress on the situation in which the denominators of rational numbers are prime numbers and describes some methods used.

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References

  1. G. Harman, On the distribution of αp modulo one, J. London Math. Soc. (2), 27 (1983), 9–18.

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  2. G. Harman, On the distribution of ap modulo one II, Proc. London Math. Soc. (3), 72 (1996), 241–260.

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  3. D. R. Heath-Brown and C. Jia, The distribution of ap modulo one, Proc. London Math. Soc. (3), 84 (2002), 79–104.

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  4. C. Jia, On the distribution of ap modulo one, J. Number Theory, 45 (1993), 241–253.

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  5. C. Jia, On the distribution of ap modulo one (II), Sci. China, Ser. A, 43 (2000), 703–721.

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  6. R. C. Vaughan, On the distribution of ap modulo 1, Mathematika, 24 (1977), 135–141.

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  7. I. M. Vinogradov, The method of trigonometric sums in the theory of numbers, translated from the Russian by K. F. Roth and A. Davenport ( WileyInterscience, London, 1954 )

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© 2002 Springer Science+Business Media Dordrecht

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Jia, C. (2002). On the Distribution of αp Modulo One. In: Kanemitsu, S., Jia, C. (eds) Number Theoretic Methods. Developments in Mathematics, vol 8. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3675-5_9

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  • DOI: https://doi.org/10.1007/978-1-4757-3675-5_9

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-5239-4

  • Online ISBN: 978-1-4757-3675-5

  • eBook Packages: Springer Book Archive

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