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Izv. Akad. Nauk SSSR Ser. Mat., 1970, Volume 34, Issue 2, Pages 299–321 (Mi izv2417)  

This article is cited in 19 scientific papers (total in 21 papers)

Sums of characters over prime numbers

A. A. Karatsuba

Abstract: In this paper we obtain a new estimate on the sum of the values $\boldsymbol\chi(p+k)$.

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English version:
Mathematics of the USSR-Izvestiya, 1970, 4:2, 303–326

Bibliographic databases:

UDC: 511
MSC: 11L40, 11L03
Received: 22.10.1969

Citation: A. A. Karatsuba, “Sums of characters over prime numbers”, Izv. Akad. Nauk SSSR Ser. Mat., 34:2 (1970), 299–321; Math. USSR-Izv., 4:2 (1970), 303–326

Citation in format AMSBIB
\by A.~A.~Karatsuba
\paper Sums of characters over prime numbers
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1970
\vol 34
\issue 2
\pages 299--321
\jour Math. USSR-Izv.
\yr 1970
\vol 4
\issue 2
\pages 303--326

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    This publication is cited in the following articles:
    1. A. A. Karatsuba, “Sums of characters with prime numbers in an arithmetic progression”, Math. USSR-Izv., 5:3 (1971), 485–501  mathnet  crossref  mathscinet  zmath
    2. A. A. Karatsuba, “Sums of Legendre symbols of polynomials of second degree over prime numbers”, Math. USSR-Izv., 12:2 (1978), 299–308  mathnet  crossref  mathscinet  zmath
    3. A. A. Karatsuba, “The distribution of pairs of quadratic residues and nonresidues of a special form”, Math. USSR-Izv., 31:2 (1988), 307–323  mathnet  crossref  mathscinet  zmath
    4. G. D. Negmatova, “The distribution of values of non-principal characters in lacunary sequences”, Russian Math. Surveys, 44:5 (1989), 214–215  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. N. M. Timofeev, “Multiplicative functions on the set of shifted prime numbers”, Math. USSR-Izv., 39:3 (1992), 1189–1207  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. Z. Kh. Rakhmonov, “A theorem on the mean value of Chebishev functions”, Russian Acad. Sci. Izv. Math., 44:3 (1995), 555–569  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. 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
    8. 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
    9. 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
    10. A. A. Kopaneva, “Otsenka korotkikh summ kharakterov Dirikhle po sdvinutym prostym chislam”, Chebyshevskii sb., 9:1 (2008), 122–143  mathnet  mathscinet
    11. Ke Gong, “On certain character sums over smooth numbers”, Glas Mat Ser III, 44:2 (2009), 333  crossref  elib
    12. 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
    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. 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
    16. Z. Kh. Rakhmonov, “Summy kharakterov s prostymi chislami”, Chebyshevskii sb., 15:2 (2014), 73–100  mathnet
    17. M. A. Korolev, “O nelineinoi summe Kloostermana”, Chebyshevskii sb., 17:1 (2016), 140–147  mathnet  mathscinet  elib
    18. 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
    19. M. A. Korolev, “Metody otsenok korotkikh summ Kloostermana”, Chebyshevskii sb., 17:4 (2016), 79–109  mathnet  crossref  mathscinet  elib
    20. 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
    21. 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
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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