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JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova

Trudy Mat. Inst. Steklov., 1980, Volume 151, Pages 3–128 (Mi tm2474)

Multiple trigonometric sums
G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov

This publication is cited in the following articles:
  1. M. A. Chahkiev, “Exact value of the exponent of convergence of the singular integral in Tarry's problem for homogeneous polynomials of degree $n$ in two variables”, Izv. Math., 85:2 (2021), 332–340  mathnet  crossref  crossref  zmath  adsnasa  isi  elib
  2. V. N. Chubarikov, A. Giyasi, “O nekotorykh problemakh analiticheskoi teorii chisel v tvorchestve G. I. Arkhipova i S. M. Voronina”, Chebyshevskii sb., 22:2 (2021), 7–26  mathnet  crossref
  3. I. Sh. Dzhabbarov, “On the Multidimensional Tarry Problem for a Cubic Polynomial”, Math. Notes, 107:5 (2020), 713–726  mathnet  crossref  crossref  mathscinet  isi  elib
  4. I. Sh. Jabbarov, “Convergence Exponent of a Special Integral in the Two-Dimensional Tarry Problem with Homogeneous Polynomial of Degree 2”, Math. Notes, 105:3 (2019), 359–365  mathnet  crossref  crossref  mathscinet  isi  elib
  5. M. A. Korolev, “The estimate of weighted Kloosterman sums by additive shift”, Doklady Mathematics (Supplementary issues), 106:2 (2022), 221–229  mathnet  crossref  crossref  elib
  6. V. N. Chubarikov, “Matematika v zhizni Gennadiya Ivanovicha Arkhipova i Sergeya Mikhailovicha Voronina”, Chebyshevskii sb., 17:1 (2016), 6–10  mathnet  elib
  7. I. F. Avdeev, “Ob otsenke dzeta-funktsii kvadratichnoi formy otritsatelnogo diskriminanta na edinichnoi pryamoi”, Chebyshevskii sb., 17:1 (2016), 23–36  mathnet  elib
  8. A. A. Karatsuba, “Comments to My Works, Written by Myself”, Proc. Steklov Inst. Math., 282, suppl. 1 (2013), S1–S23  mathnet  crossref  crossref  isi  elib
  9. I. Sh. Dzhabbarov, “O pokazatele skhodimosti osobogo integrala mnogomernoi problemy Terri”, Chebyshevskii sb., 14:2 (2013), 74–103  mathnet
  10. V. N. Chubarikov, “Matematicheskaya zhizn G. I. Arkhipova”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 13:4(2) (2013), 5–23  mathnet  crossref
  11. G. I. Arkhipov, S. B. Gashkov, M. P. Mineev, S. M. Nikolskii, V. A. Sadovnichii, “O matematicheskikh rabotakh Vladimira Nikolaevicha Chubarikova”, Diskret. matem., 24:2 (2012), 4–20  mathnet  crossref  mathscinet  elib
  12. 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
  13. D. A. Popov, “On the second term in the Weyl formula for the spectrum of the Laplace operator on the two-dimensional torus and the number of integer points in spectral domains”, Izv. Math., 75:5 (2011), 1007–1045  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  14. V. N. Chubarikov, “Mnogomernye problemy teorii prostykh chisel”, Chebyshevskii sb., 12:4 (2011), 174–263  mathnet  mathscinet
  15. I. Sh. Dzhabarov, “Ob otsenkakh trigonometricheskikh integralov”, Chebyshevskii sb., 11:1 (2010), 85–108  mathnet  mathscinet
  16. L. D. Pustyl'nikov, “Generalized continued fractions and ergodic theory”, Russian Math. Surveys, 58:1 (2003), 109–159  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
  17. Chakhkiev M.A., “The exponent of convergence of the singular integral in a multidimensional analog of the Terry problem”, Doklady Mathematics, 67:3 (2003), 320–322  isi
  18. 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
  19. D. A. Popov, “Estimates with constants for some classes of oscillatory integrals”, Russian Math. Surveys, 52:1 (1997), 73–145  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
  20. L. D. Pustyl'nikov, “Generalized continued fractions and estimates of Weyl sums and the remainder term in the distribution law for the fractional parts of the values of a polynomial”, Math. Notes, 56:6 (1994), 1315–1317  mathnet  crossref  mathscinet  zmath  isi
  21. L. D. Pustyl'nikov, “Distribution of the fractional parts of a polynomial, Weyl sums, and ergodic theory”, Russian Math. Surveys, 48:4 (1993), 143–179  mathnet  crossref  mathscinet  zmath  adsnasa  isi
  22. L. V. Kiseleva, “On the number of zeros of the function $\zeta(s)$ on “almost all” short intervals of the critical line”, Math. USSR-Izv., 32:3 (1989), 475–499  mathnet  crossref  mathscinet  zmath
  23. Oskolkov K.I., “On the Properties of a Class of Vinogradov,I.M. Series”, Doklady Akademii Nauk Sssr, 300:4 (1988), 803–807  mathnet  isi
  24. O. V. Tyrina, “A new estimate for a trigonometric integral of I. M. Vinogradov”, Math. USSR-Izv., 30:2 (1988), 337–351  mathnet  crossref  mathscinet  zmath
  25. Arkhipov G.I., Karatsuba A.A., “Warnig Problem Multidimensional Analog”, Doklady Akademii Nauk Sssr, 295:3 (1987), 521–523  mathnet  isi
  26. D. A. Mit'kin, “An estimate of the number of terms in Waring's problem for polynomials of general form”, Math. USSR-Izv., 29:2 (1987), 371–406  mathnet  crossref  mathscinet  zmath
  27. Chubarikov V.N., “A Multidimensional Additive Problem with Prime–Numbers”, Doklady Akademii Nauk Sssr, 290:4 (1986), 805–808  mathnet  isi
  28. V. N. Chubarikov, “Estimates of multiple trigonometric sums with prime numbers”, Math. USSR-Izv., 27:2 (1986), 323–357  mathnet  crossref  mathscinet  zmath
  29. Arkhipov G.I., Chubarikov V.N., “The Arithmetical Conditions of the Solvability of Diophantine Nonlinear Equation Systems”, Doklady Akademii Nauk Sssr, 284:1 (1985), 16–21  mathnet  isi
  30. G. I. Arkhipov, “On he Hilbert–Kamke problem”, Math. USSR-Izv., 24:1 (1985), 1–47  mathnet  crossref  mathscinet  zmath
  31. G. I. Arkhipov, A. N. Zhitkov, “On Waring's problem with nonintegral exponent”, Math. USSR-Izv., 25:3 (1985), 443–454  mathnet  crossref  mathscinet  zmath
  32. Chubarikov V.N., “Multiple Trigonometric Sums with Prime–Numbers”, Doklady Akademii Nauk Sssr, 278:2 (1984), 302–304  mathnet  isi
  33. G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, “Special cases of the theory of multiple trigonometric sums”, Math. USSR-Izv., 23:1 (1984), 17–82  mathnet  crossref  mathscinet  zmath
  34. Arkhipov G.I., Karatsuba A.A., Chubarikov V.N., “New Uniform Estimations of Multiple Trigonometric Sums”, Doklady Akademii Nauk Sssr, 272:1 (1983), 11–12  mathnet  isi
  35. G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, “Multiple trigonometric sums and their applications”, Math. USSR-Izv., 17:1 (1981), 1–54  mathnet  crossref  mathscinet  zmath  isi
  36. Arkhipov G.I., Karatsuba A.A., Chubarikov V.N., “Uniform Estimates of Multiple Trigonometric Sums”, Doklady Akademii Nauk Sssr, 252:6 (1980), 1289–1291  isi
  37. Arkhipov G.I., Karatsuba A.A., Chubarikov V.N., “On a System of Diophantine Equations”, Doklady Akademii Nauk Sssr, 252:2 (1980), 275–276  isi


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