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Estimates of trigonometric sums modulo p r

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Bibliography

  1. I. M. Vinogradov, Selected Works [in Russian], Izd. AN SSSR, Moscow, 1952.

    Google Scholar 

  2. I. M. Vinogradov, The Method of Trigonometric Sums in Number Theory [in Russian], 2nd edition, Nauka, Moscow, 1980.

    MATH  Google Scholar 

  3. I. M. Vinogradov, Special Versions of the Method of Trigonometric Sums [in Russian], Nauka, Moscow, 1976.

    Google Scholar 

  4. A. A. Karatsuba Izv. Ross. Akad. Nauk Ser. Mat. [Russian Acad. Sci. Izv. Math.], 59 (1995), no. 4, 61–80.

    MathSciNet  Google Scholar 

  5. A. A. Karatsuba Izv. Ross. Akad. Nauk Ser. Mat. [Russian Acad. Sci. Izv. Math.], 59 (1995), no. 5, 93–102.

    MathSciNet  Google Scholar 

  6. J. Friedlander and H. Iwaniec, The Brun-Titchmarsh Theorem, Lecture Notes in Statist., vol. 247, Cambridge Univ. Press, Cambridge, 1997.

    Google Scholar 

  7. S. Konyagin and I. Shparlinski, Character Sums with Exponential Functions, Cambridge Univ. Press, Cambridge, 1999.

    MATH  Google Scholar 

  8. S. V. Konyagin in: IV International Conference “Problems of Current Interest in Number Theory and its Applications”, Topical Problems, pt. III [in Russian], Moscow, 2002, pp. 86–114.

  9. D. R. Heath-Brown and S. V. Konyagin Quart. J. Math., 51 (2000), 221–235.

    Article  MathSciNet  Google Scholar 

  10. Yu. V. Malykhin, “Estimates of trigonometric sums modulo p 2,” (to appear).

  11. J. Bourgain and S. V. Konyagin C. R. Math. Acad. Sci. Paris, 337 (2003), no. 2, 75–80.

    MathSciNet  Google Scholar 

  12. J. Bourgain and Mei-Chu Chang C. R. Math. Acad. Sci. Paris, 339 (2004), no. 7, 463–466.

    MathSciNet  Google Scholar 

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Translated from Matematicheskie Zametki, vol. 80, no. 5, 2006, pp. 793–796.

Original Russian Text Copyright © 2006 by Yu. V. Malykhin.

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Malykhin, Y.V. Estimates of trigonometric sums modulo p r . Math Notes 80, 748–752 (2006). https://doi.org/10.1007/s11006-006-0197-1

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