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Izv. RAN. Ser. Mat., 1995, Volume 59, Issue 4, Pages 61–80 (Mi izv31)  

This article is cited in 34 scientific papers (total in 35 papers)

Fractional parts of functions of a special form

A. A. Karatsuba

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: This paper contains proofs of theorems on the distribution of fractional parts of functions connected with inverse values modulo a given number.

Full text: PDF file (1349 kB)
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English version:
Izvestiya: Mathematics, 1995, 59:4, 721–740

Bibliographic databases:

MSC: 11N45
Received: 06.01.1995

Citation: A. A. Karatsuba, “Fractional parts of functions of a special form”, Izv. RAN. Ser. Mat., 59:4 (1995), 61–80; Izv. Math., 59:4 (1995), 721–740

Citation in format AMSBIB
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\paper Fractional parts of functions of a~special form
\jour Izv. RAN. Ser. Mat.
\yr 1995
\vol 59
\issue 4
\pages 61--80
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\transl
\jour Izv. Math.
\yr 1995
\vol 59
\issue 4
\pages 721--740
\crossref{https://doi.org/10.1070/IM1995v059n04ABEH000031}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Karatsuba, “Analogues of Kloosterman sums”, Izv. Math., 59:5 (1995), 971–981  mathnet  crossref  mathscinet  zmath  isi
    2. A. A. Karatsuba, “Double Kloosterman sums”, Math. Notes, 66:5 (1999), 565–569  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. M. A. Korolev, “Incomplete Kloosterman sums and their applications”, Izv. Math., 64:6 (2000), 1129–1152  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Cobeli C., Zaharescu A., “Distribution of a Sparse Set of Fractions Modulo Q”, Bull. London Math. Soc., 33:Part 2 (2001), 138–148  crossref  mathscinet  zmath  isi
    5. Banks W. Harcharras A. Shparlinski I., “Short Kloosterman Sums for Polynomials Over Finite Fields”, Can. J. Math.-J. Can. Math., 55:2 (2003), 225–246  crossref  mathscinet  zmath  isi
    6. Yu. V. Malykhin, “Bounds for exponential sums modulo $p^2$”, J. Math. Sci., 146:2 (2007), 5686–5696  mathnet  crossref  mathscinet  zmath  elib  elib
    7. Banks W.D., Heath-Brown R., Shparlinski I.E., “On the average value of divisor sums in arithmetic progressions”, International Mathematics Research Notices, 2005, no. 1, 1–25  crossref  mathscinet  zmath  isi  elib
    8. J. BOURGAIN, “MORE ON THE SUM-PRODUCT PHENOMENON IN PRIME FIELDS AND ITS APPLICATIONS”, Int. J. Number Theory, 01:01 (2005), 1  crossref
    9. Garaev M., “Double Exponential Sums Related to Diffie-Hellman Distributions”, Int. Math. Res. Notices, 2005, no. 17, 1005–1014  crossref  mathscinet  zmath  isi
    10. Garaev M. Luca F. Shparlinski I., “Exponential Sums and Congruences with Factorials”, J. Reine Angew. Math., 584 (2005), 29–44  crossref  mathscinet  zmath  isi
    11. A. A. Glibichuk, “Combinational properties of sets of residues modulo a prime and the Erdős–Graham problem”, Math. Notes, 79:3 (2006), 356–365  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    12. Yu. V. Malykhin, “Estimates of trigonometric sums modulo $p^r$”, Math. Notes, 80:5 (2006), 748–752  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    13. Bourgain J., Glibichuk A., Konyagin S., “Estimates for the Number of Sums and Products and for Exponential Sums in Fields of Prime Order”, J. Lond. Math. Soc.-Second Ser., 73:2 (2006), 380–398  crossref  mathscinet  zmath  isi
    14. Shparlinski I.E., “Bounds of incomplete multiple Kloosterman sums”, Journal of Number Theory, 126:1 (2007), 68–73  crossref  mathscinet  zmath  isi
    15. Shparlinski I.E., “Distribution of Points on Modular Hyperbolas”, Number Theory: Sailing on the Sea of Number Theory, Series on Number Theory and its Applications, 2, 2007, 155–189  isi
    16. Banks W.D. Garaev M.Z. Luca F. Shparlinski I.E., “Uniform Distribution of Fractional Parts Related to Pseudoprimes”, Can. J. Math.-J. Can. Math., 61:3 (2009), 481–502  crossref  mathscinet  zmath  isi
    17. V. V. Krasil'shchikov, “The spectrum of one-dimensional quasilattices”, Siberian Math. J., 51:1 (2010), 53–56  mathnet  crossref  mathscinet  isi  elib  elib
    18. M. Z. Garaev, “Estimation of Kloosterman Sums with Primes and Its Application”, Math. Notes, 88:3 (2010), 330–337  mathnet  crossref  crossref  mathscinet  isi
    19. A. A. Karatsuba, “New Estimates of Short Kloosterman Sums”, Math. Notes, 88:3 (2010), 347–359  mathnet  crossref  crossref  mathscinet  isi
    20. M. A. Korolev, “Short Kloosterman Sums with Weights”, Math. Notes, 88:3 (2010), 374–385  mathnet  crossref  crossref  mathscinet  zmath  isi
    21. Alkan E. Xiong M. Zaharescu A., “Pair Correlation of Sums of Rationals with Bounded Height”, J. Reine Angew. Math., 641 (2010), 21–67  crossref  mathscinet  zmath  isi
    22. S. A. Gritsenko, E. A. Karatsuba, M. A. Korolev, I. S. Rezvyakova, D. I. Tolev, M. E. Changa, “Scientific Achievements of Anatolii Alekseevich Karatsuba”, Proc. Steklov Inst. Math., 280, suppl. 2 (2013), S1–S22  mathnet  crossref  crossref  zmath  isi  elib
    23. Shparlinski I.E., “Modular Hyperbolas”, Jap. J. Math., 7:2 (2012), 235–294  crossref  isi
    24. J. Bourgain, M. Z. Garaev, “Sumsets of reciprocals in prime fields and multilinear Kloosterman sums”, Izv. Math., 78:4 (2014), 656–707  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    25. Bourgain J. Garaev M.Z., “Kloosterman Sums in Residue Rings”, Acta Arith., 164:1 (2014), 43–64  crossref  isi
    26. Shparlinski I.E., “Points on Varieties Over Finite Fields in Small Boxes”, Scholar - a Scientific Celebration Highlighting Open Lines of Arithmetic Research, Contemporary Mathematics, 655, ed. Cojocaru A. David C. Pappalardi F., Amer Mathematical Soc, 2015, 209–233  crossref  isi
    27. M. A. Korolev, “Karatsuba's method for estimating Kloosterman sums”, Sb. Math., 207:8 (2016), 1142–1158  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    28. M. A. Korolev, “On Short Kloosterman Sums Modulo a Prime”, Math. Notes, 100:6 (2016), 820–827  mathnet  crossref  crossref  mathscinet  isi  elib
    29. M. A. Korolev, “Metody otsenok korotkikh summ Kloostermana”, Chebyshevskii sb., 17:4 (2016), 79–109  mathnet  crossref  mathscinet  elib
    30. M. A. Korolev, “Generalized Kloosterman sum with primes”, Proc. Steklov Inst. Math., 296 (2017), 154–171  mathnet  crossref  crossref  mathscinet  isi  elib
    31. S. V. Konyagin, M. A. Korolev, “Irreducible solutions of an equation involving reciprocals”, Sb. Math., 208:12 (2017), 1818–1834  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    32. M. A. Korolev, “On Anatolii Alekseevich Karatsuba's works written in the 1990s and 2000s”, Proc. Steklov Inst. Math., 299 (2017), 1–43  mathnet  crossref  crossref  isi  elib  elib
    33. M. A. Korolev, “On a Diophantine inequality with reciprocals”, Proc. Steklov Inst. Math., 299 (2017), 132–142  mathnet  crossref  crossref  isi  elib  elib
    34. M. A. Korolev, “Kloosterman sums with multiplicative coefficients”, Izv. Math., 82:4 (2018), 647–661  mathnet  crossref  crossref  adsnasa  isi  elib
    35. M. A. Korolev, “Divisors of a quadratic form with primes”, Proc. Steklov Inst. Math., 303 (2018), 154–170  mathnet  crossref  crossref  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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