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A. A. Karatsuba, “The multidimensional Dirichlet divisor problem and zero free regions for the Riemann zeta function,” Funct. Approx. Comment. Math. 28, 131–140 (2000).
A. A. Karatsuba, “On the relationship between the multidimensional Dirichlet divisor problem and the boundary of zeros of ζ(s),” Mat. Zametki 70(3), 477–480 (2001) [Math. Notes 70 (3), 432–435 (2001)].
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A. A. Karatsuba, “Sums of characters and primitive roots in finite fields,” Dokl. Akad. Nauk SSSR 180(6), 1287–1289 (1968).
A. A. Karatsuba, “Estimates of character sums,” Izv. Akad. Nauk SSSR, Ser. Mat. 34(1), 20–30 (1970) [Math. USSR-Izv. 4 (1), 19–29 (1970)].
A. A. Karatsuba, “Sums of characters over prime numbers,” Izv. Akad. Nauk SSSR, Ser. Mat. 34(2), 299–321 (1970) [Math. USSR-Izv. 4 (2), 303–326 (1970)].
I. M. Vinogradov, “An Estimate for a certain sum extended over the primes of an arithmetic progression,” Izv. Akad. Nauk SSSR, Ser. Mat. 30(3), 481–496 (1966).
A. A. Karatsuba, “Sums of characters in sequences of shifted prime numbers, with applications,” Mat. Zametki 17(1), 155–159 (1975) [Math. Notes 17 (1), 91–93 (1975)].
A. A. Karatsuba, “The distribution of products of shifted prime numbers in arithmetic progressions,” Dokl. Akad. Nauk SSSR 192(4), 724–727 (1970).
A. A. Karatsuba, “Lower estimates of sums of polynomial characters,” Mat. Zametki 14(1), 67–72 (1973) [Math. Notes 14 (1), 593–596 (1973)].
A. A. Karatsuba, “Sums of Legendre symbols of polynomials of second degree over prime numbers,” Izv. Akad. Nauk SSSR, Ser. Mat. 42(2), 315–324 (1978) [Math. USSR-Izv. 12 (2), 299–308 (1978)].
A. A. Karatsuba, “Distribution of values of nonprincipal characters,” Tr. Mat. Inst. im. V.A. Steklova, Akad. Nauk SSSR 142, 156–164 (1976) [Proc. Steklov Inst. Math. 142, 165–174 (1979)].
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A. A. Karatsuba, “Approximation of exponential sums by shorter ones,” Proc. Indian Acad. Sci. Math. Sci. 97(1–3), 167–178 (1987).
I. M. Vinogradov, “On the mean value of the number of classes of purely root forms of a negative determinant,” Soobshch. Kharkov. Mat. O-va 16(1–2), 10–38 (1918).
J. G. van der Corput, “Verschärfung der Abschätzung beim Teilerproblem,” Math. Ann. 87(1–2), 39–65 (1922).
A. A. Karatsuba and M. A. Korolev, “A theorem on the approximation of a trigonometric sum by a shorter one,” Izv. Ross. Akad. Nauk, Ser. Mat. 71(2), 123–150 (2007) [Izv.: Math. 71 (2), 341–370 (2007)].
A. A. Karatsuba and E. A. Karatsuba, “Applications of ATS in a quantum-optical model,” in Analysis and Mathematical Physics (Birkhäuser, Basel, 2009), pp. 211–232.
A. A. Karatsuba and E. A. Karatsuba, “A resummation formula for collapse and revival in the Jaynes-Cummings model,” J. Phys. A: Math. Theor. 42(19), 195304 (2009).
E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen (Teubner, Leipzig, 1909), Vol. 2.
M. E. Changa, “Numbers whose prime divisors lie in special intervals,” Izv. Ross. Akad. Nauk, Ser. Mat. 67(4), 213–224 (2003) [Izv.: Math. 67 (4), 837–848 (2003)].
A. A. Karatsuba, “On a property of the set of primes as a multiplicative basis of natural numbers,” Dokl. Akad. Nauk 439(2), 159–162 (2011) [Dokl. Math. 84 (1), 467–470 (2011)].
A. A. Karatsuba, “A property of the set of prime numbers,” Uspekhi Mat. Nauk 66(2), 3–14 (2011) [Russ. Math. Surveys 66 (2), 209–220 (2011)].
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Original Russian Text © M.E. Changa, S.A. Gritsenko, E.A. Karatsuba, M.A. Korolev, I.S. Rezvyakova, D.I. Tolev, 2012, published in Sovremennye Problemy Matematiki, 2012, Vol. 16, pp. 7–30.
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Changa, M.E., Gritsenko, S.A., Karatsuba, E.A. et al. Scientific achievements of Anatolii Alekseevich Karatsuba. Proc. Steklov Inst. Math. 280 (Suppl 2), 1–22 (2013). https://doi.org/10.1134/S0081543813030012
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DOI: https://doi.org/10.1134/S0081543813030012