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Mathematics of the USSR-Izvestiya, 1970, Volume 4, Issue 2, Pages 303–326
DOI: https://doi.org/10.1070/IM1970v004n02ABEH000907
(Mi im2417)
 

This article is cited in 24 scientific papers (total in 26 papers)

Sums of characters over prime numbers

A. A. Karatsuba
References:
Abstract: In this paper we obtain a new estimate on the sum of the values χ(p+k).
Received: 22.10.1969
Bibliographic databases:
Document Type: Article
UDC: 511
MSC: 11L40, 11L03
Language: English
Original paper language: Russian
Citation: A. A. Karatsuba, “Sums of characters over prime numbers”, Math. USSR-Izv., 4:2 (1970), 303–326
Citation in format AMSBIB
\Bibitem{Kar70}
\by A.~A.~Karatsuba
\paper Sums of characters over prime numbers
\jour Math. USSR-Izv.
\yr 1970
\vol 4
\issue 2
\pages 303--326
\mathnet{http://mi.mathnet.ru/eng/im2417}
\crossref{https://doi.org/10.1070/IM1970v004n02ABEH000907}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=271040}
\zmath{https://zbmath.org/?q=an:0246.10021}
Linking options:
  • https://www.mathnet.ru/eng/im2417
  • https://doi.org/10.1070/IM1970v004n02ABEH000907
  • https://www.mathnet.ru/eng/im/v34/i2/p299
  • This publication is cited in the following 26 articles:
    1. Z. Kh. Rakhmonov, “Raspredelenie proizvedenii sdvinutykh prostykh chisel v arifmeticheskikh progressiyakh s rastuschei raznostyu”, Chebyshevskii sb., 23:3 (2022), 156–168  mathnet  crossref
    2. A. A. Karatsuba, “Five Lectures on the Life and Work of Academician I. M. Vinogradov”, Proc. Steklov Inst. Math., 314 (2021), 1–26  mathnet  crossref  crossref  isi  elib
    3. Bryce Kerr, “Bounds of Multiplicative Character Sums over Shifted Primes”, Proc. Steklov Inst. Math., 314 (2021), 64–89  mathnet  crossref  crossref  isi  elib
    4. V. N. Chubarikov, “Srednee znachenie proizvedenii simvolov Lezhandra po prostym”, Chebyshevskii sb., 20:2 (2019), 336–347  mathnet  crossref
    5. Zarullo Rakhmonov, Irregularities in the Distribution of Prime Numbers, 2018, 187  crossref
    6. 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  mathscinet  isi  elib  elib
    7. 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
    8. M. A. Korolev, “On non-linear Kloosterman sum”, Doklady Mathematics (Supplementary issues), 106:2 (2022), 246–249  mathnet  crossref  mathscinet  elib
    9. Z. Kh. Rakhmonov, Sh. Kh. Mirzorakhimov, “Summy kharakterov po modulyu svobodnogo ot kubov na sdvinutykh prostykh”, Chebyshevskii sb., 17:1 (2016), 201–216  mathnet  elib
    10. M. A. Korolev, “Methods of estimating of incomplete Kloosterman sums”, Doklady Mathematics (Supplementary issues), 106:2 (2022), 230–245  mathnet  crossref  crossref  mathscinet  elib
    11. Z. Kh. Rakhmonov, “Summy kharakterov s prostymi chislami”, Chebyshevskii sb., 15:2 (2014), 73–100  mathnet
    12. Z. Kh. Rakhmonov, “Raspredelenie znachenii kharakterov Dirikhle v posledovatelnosti sdvinutykh prostykh chisel”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 13:4(2) (2013), 113–117  mathnet  crossref  elib
    13. 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
    14. Shparlinski I.E., “Modular Hyperbolas”, Jap. J. Math., 7:2 (2012), 235–294  crossref  isi
    15. J. B. Friedlander, K. Gong, I. E. Shparlinski, “Character Sums over Shifted Primes”, Math. Notes, 88:4 (2010), 585–598  mathnet  crossref  crossref  mathscinet  isi
    16. Ke Gong, “On certain character sums over smooth numbers”, Glas Mat Ser III, 44:2 (2009), 333  crossref  elib
    17. 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
    18. A. A. Kopaneva, “Otsenka korotkikh summ kharakterov Dirikhle po sdvinutym prostym chislam”, Chebyshevskii sb., 9:1 (2008), 122–143  mathnet  mathscinet
    19. N. G. Moshchevitin, “Sets of the form $\mathscr A+\mathscr B$ and finite continued fractions”, Sb. Math., 198:4 (2007), 537–557  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    20. G. I. Arkhipov, V. I. Blagodatskikh, V. S. Vladimirov, S. M. Voronin, O. B. Lupanov, E. F. Mishchenko, Yu. V. Prokhorov, V. N. Chubarikov, A. B. Shidlovskii, “Anatolii Alekseevich Karatsuba (on his 60th birthday)”, Russian Math. Surveys, 53:2 (1998), 419–422  mathnet  crossref  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:812
    Russian version PDF:326
    English version PDF:32
    References:87
    First page:1
     
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