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Izv. RAN. Ser. Mat., 2000, Volume 64, Issue 2, Pages 29–42 (Mi izv283)  

This article is cited in 12 scientific papers (total in 13 papers)

Weighted character sums

A. A. Karatsuba

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Weighted sums of Dirichlet characters are estimated with power reduction when the number of terms in the sum is small in comparison with the absolute value of the character.

DOI: https://doi.org/10.4213/im283

Full text: PDF file (836 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2000, 64:2, 249–263

Bibliographic databases:

MSC: 11L03, 11N37, 11L40, 11L99
Received: 28.10.1999

Citation: A. A. Karatsuba, “Weighted character sums”, Izv. RAN. Ser. Mat., 64:2 (2000), 29–42; Izv. Math., 64:2 (2000), 249–263

Citation in format AMSBIB
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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. Banks W.D., Heath-Brown R., Shparlinski I.E., “On the average value of divisor sums in arithmetic progressions”, Int. Math. Res. Not., 2005, no. 1, 1–25  crossref  mathscinet  zmath  isi  elib
    2. Garaev M.Z., Karatsuba A.A., “On character sums and the exceptional set of a congruence problem”, J. Number Theory, 114:1 (2005), 182–192  crossref  mathscinet  zmath  isi  elib  scopus
    3. A. A. Karatsuba, “Arithmetic problems in the theory of Dirichlet characters”, Russian Math. Surveys, 63:4 (2008), 641–690  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. Chang Mei-Chu, “On a question of Davenport and Lewis and new character sum bounds in finite fields”, Duke Math. J., 145:3 (2008), 409–442  crossref  mathscinet  zmath  isi  elib  scopus
    5. Chang M.-Ch., “Character Sums in Finite Fields”, Finite Fields: Theory and Applications, Contemporary Mathematics, 518, 2010, 83–98  crossref  mathscinet  zmath  isi
    6. M. Z. Garaev, S. V. Konyagin, Yu. V. Malykhin, “Asymptotics for the sum of powers of distances between power residues modulo a prime”, Proc. Steklov Inst. Math., 276 (2012), 77–89  mathnet  crossref  mathscinet  isi  elib  elib
    7. 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
    8. Proc. Steklov Inst. Math., 280 (2013), 61–90  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    9. Chang M.-Ch., Shparlinski I.E., “Double Character Sums Over Subgroups and Intervals”, Bull. Aust. Math. Soc., 90:3 (2014), 376–390  crossref  mathscinet  zmath  isi  scopus
    10. 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  mathscinet  zmath  isi
    11. M. A. Korolev, “O nelineinoi summe Kloostermana”, Chebyshevskii sb., 17:1 (2016), 140–147  mathnet  mathscinet  elib
    12. A. S. Volostnov, I. D. Shkredov, “Sums of multiplicative characters with additive convolutions”, Proc. Steklov Inst. Math., 296 (2017), 256–269  mathnet  crossref  crossref  mathscinet  isi  elib
    13. 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
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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