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On exponential sums studied by Indlekofer and Kátai

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Abstract

We continue the study of sums of the form

$$ \sum\limits_{m_j p \leqq x} {Y_{mj} X_p e(\alpha m_j p)} , $$

begun by Indlekofer and Kátai. Here |Y n |,|X p | ≦ 1 and α is irrational. We prove one conjecture of Kátai, disprove another by both authors, and give what may be a close to best possible result valid for all irrational α.

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References

  1. H. Davenport, Multiplicative Number Theory, second edition (revised by H. L. Montgomery), Springer (New York, 1980).

    MATH  Google Scholar 

  2. G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th Edition, Oxford University Press (Oxford, 1979).

    MATH  Google Scholar 

  3. K.-H. Indlekofer and I. Kátai, Some remarks on trigonometric sums, Acta Math. Hungar., 118 (2008), 313–318.

    Article  MATH  MathSciNet  Google Scholar 

  4. I. Kátai, A remark on trigonometric sums, Acta Math. Hungar., 112 (2006), 221–225.

    Article  MATH  MathSciNet  Google Scholar 

  5. I. Kátai, Some remarks on a theorem of H. Daboussi, preprint.

  6. Huixue Lao, A remark on a trigonometric sum, Acta Arith., 134 (2008), 127–131.

    Article  MATH  MathSciNet  Google Scholar 

  7. H. L. Montgomery and R. C. Vaughan, On the large sieve, Mathematika, 20 (1973), 119–134.

    MATH  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  9. R. C. Vaughan, The Hardy-Littlewood Method, Cambridge Tracts in Mathematics, 80, Cambridge University Press (Cambridge, 1980).

    Google Scholar 

  10. I. M. Vinogradov, The Method of Trigonometric Sums in the Theory of Numbers, translated from the Russian, revised and annotated by K. F. Roth and Anne Davenport, Reprint of the 1954 translation, Dover Publications, Inc. (Mineola, NY, 2004).

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, UK

    G. Harman

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  1. G. Harman
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Correspondence to G. Harman.

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Harman, G. On exponential sums studied by Indlekofer and Kátai. Acta Math Hung 124, 289–298 (2009). https://doi.org/10.1007/s10474-009-8192-0

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  • DOI: https://doi.org/10.1007/s10474-009-8192-0

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