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On the Distribution of αp Modulo One

  • Chaohua Jia
Part of the Developments in Mathematics book series (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.

Keywords

prime number sieve method trigonometric sum 

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References

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    G. Harman, On the distribution of αp modulo one, J. London Math. Soc. (2), 27 (1983), 9–18.MathSciNetzbMATHCrossRefGoogle Scholar
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    C. Jia, On the distribution of ap modulo one, J. Number Theory, 45 (1993), 241–253.MathSciNetzbMATHCrossRefGoogle Scholar
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    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 )Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Chaohua Jia
    • 1
  1. 1.Institute of MathematicsAcademia SinicaBeijingP. R. China

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