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Uspekhi Mat. Nauk, 2008, Volume 63, Issue 4(382), Pages 43–92 (Mi umn9234)  

This article is cited in 11 scientific papers (total in 12 papers)

Arithmetic problems in the theory of Dirichlet characters

A. A. Karatsuba

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: A survey of results related to the distribution of values of Dirichlet characters on sparse sets of positive integers is presented.

DOI: https://doi.org/10.4213/rm9234

Full text: PDF file (849 kB)
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English version:
Russian Mathematical Surveys, 2008, 63:4, 641–690

Bibliographic databases:

UDC: 511
MSC: 11L40, 11L20
Received: 10.03.2008

Citation: A. A. Karatsuba, “Arithmetic problems in the theory of Dirichlet characters”, Uspekhi Mat. Nauk, 63:4(382) (2008), 43–92; Russian Math. Surveys, 63:4 (2008), 641–690

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. Gong Ke, “On certain character sums over smooth numbers”, Glas. Mat. Ser. III, 44(64):2 (2009), 333–342  crossref  mathscinet  zmath  isi  elib  scopus
    2. Garaev M.Z., Shen Chun-Yen, “On the size of the set $A(A+1)$”, Math. Z., 265:1 (2010), 125–132  crossref  mathscinet  zmath  elib  scopus
    3. L. A. Bassalygo, V. A. Zinov'ev, “Exact Values of the Sums of Multiplicative Characters of Polynomials over Finite Fields”, Math. Notes, 88:3 (2010), 308–316  mathnet  crossref  crossref  mathscinet  isi
    4. 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
    5. Proc. Steklov Inst. Math., 280 (2013), 61–90  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    6. 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
    7. Justus B., “The Distribution of Quadratic Residues and Nonresidues in Arithmetic Progressions”, Lith. Math. J., 54:2 (2014), 142–149  crossref  mathscinet  zmath  isi  scopus
    8. Shkredov I.D., “Sumsets in Quadratic Residues”, Acta Arith., 164:3 (2014), 221–243  crossref  mathscinet  zmath  isi  scopus
    9. 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
    10. 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
    11. Z. Kh. Rakhmonov, “Sums of values of nonprincipal characters over a sequence of shifted primes”, Proc. Steklov Inst. Math., 299 (2017), 219–245  mathnet  crossref  crossref  isi  elib
    12. A. S. Volostnov, “On Double Sums with Multiplicative Characters”, Math. Notes, 104:2 (2018), 197–203  mathnet  crossref  crossref  isi  elib
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