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Karatsuba, Anatoliĭ Alekseevich

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Author ID: karatsuba.anatolij-alekseevich Recent zbMATH articles by "Karatsuba, Anatoliĭ Alekseevich"
Published as: Karatsuba, A.; Karatsuba, A. A.; Karatsuba, A.a.; Karatsuba, Anatolii A.; Karatsuba, Anatolij A.; Karatsuba, Anatolij Alekseevich; Karatsuba, Anatoliĭ A.
Homepage: http://www.mi.ras.ru/~karatsuba/index_e.html
External Links: MGP · Math-Net.Ru · Wikidata · dblp · GND
Documents Indexed: 201 Publications since 1960, including 10 Books
Biographic References: 13 Publications
all top 5

Co-Authors

149 single-authored
28 Arkhipov, Gennadiĭ Ivanovich
20 Chubarikov, Vladimir Nikolaevich
4 Karatsuba, Ekaterina Anatol’evna
4 Korolëv, Maksim Aleksandrovich
3 Blagodatskikh, Viktor Ivanovich
3 Garaev, Moubariz Z.
2 Kudryavtsev, Lev Dmitrievich
2 Prokhorov, Yuriĭ Vasil’evich
2 Shafarevich, Igor’ Rostislavovich
2 Vinogradov, Ivan Matveevich
2 Vladimirov, Vasiliĭ Sergeevich
2 Voronin, Sergeĭ Mikhaĭlovich
1 Arkhontova, R. A.
1 Bakhtin, Ivan Alekseevich
1 Baskakov, Anatoliĭ Grigor’evich
1 Belyaeva, È. S.
1 Bolibrukh, Andreĭ Andreevich
1 Borisovich, Yuriĭ Grigor’evich
1 Chirskiĭ, Vladimir Grigor’evich
1 Chubarkov, V. N.
1 Dezin, Alekseĭ Alekseevich
1 Fomenko, Anatoliĭ Timofeevich
1 Galin, G. Ya.
1 Galochkin, A. I.
1 Grechenko, A. S.
1 Iskovskikh, Vasiliĭ Alekseevich
1 Korobov, Nikolaĭ Mikhaĭlovich
1 Kovalevskaya, Èlla Ivanovna
1 Kubilius, Jonas
1 Kudinov, Anatoly Filippovich
1 Latyshev, Viktor Nikolaevich
1 Lukashenko, Taras P.
1 Lupanov, Oleg Borisovich
1 Makarov, Yu. N.
1 Mineev, Mikhail Petrovich
1 Nesterenko, Yuriĭ Valentinovich
1 Nikol’skiĭ, Sergeĭ Mikhaĭlovich
1 Novák, Břetislav
1 Obukhovskiĭ, Valeriĭ Vladimirovich
1 Oskolkov, Konstantin Ilyich
1 Perov, Anatolij Ivanovich
1 Porubsky, Stefan
1 Postnikova, L. P.
1 Potapov, A. S.
1 Potapov, Mikhaĭl Konstantinovich
1 Rokyta, Mirko
1 Semënov, Evgeniĭ Mikhaĭlovich
1 Shidlovskiĭ, Andrei Borisovich
1 Trofimov, V. P.
1 Udodenko, N. N.
1 Vlášek, Zdeněk
1 Yudin, Aleksandr Aleksandrovich
1 Zachepa, V. R.
all top 5

Serials

26 Soviet Mathematics. Doklady
19 Mathematics of the USSR. Izvestiya
18 Mathematical Notes
18 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya
16 Russian Mathematical Surveys
14 Proceedings of the Steklov Institute of Mathematics
8 Izvestiya: Mathematics
8 Doklady Mathematics
5 Matematicheskie Zametki
5 Chebyshevskiĭ Sbornik
5 Trudy Matematicheskogo Instituta Imeni V. A. Steklova
4 Vestnik Moskovskogo Universiteta. Seriya I. Matematika, Mekhanika
3 Uspekhi Matematicheskikh Nauk [N. S.]
3 Acta Arithmetica
2 Functiones et Approximatio. Commentarii Mathematici
2 Elektronische Informationsverarbeitung und Kybernetik
2 Tatra Mountains Mathematical Publications
2 Russian Academy of Sciences. Izvestiya. Mathematics
2 De Gruyter Expositions in Mathematics
2 Translations. Series 2. American Mathematical Society
1 Problems of Information Transmission
1 Archiv der Mathematik
1 Journal of Number Theory
1 Matematicheskiĭ Sbornik. Novaya Seriya
1 Mathematica Slovaca
1 Proceedings of the Edinburgh Mathematical Society. Series II
1 Transactions of the Moscow Mathematical Society
1 Trudy Moskovskogo Matematicheskogo Obshchestva
1 Pokroky Matematiky, Fyziky & Astronomie
1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
1 Izvestiya Rossiĭskoĭ Akademii Nauk. Seriya Matematicheskaya
1 Russian Academy of Sciences. Doklady. Mathematics
1 Acta Mathematica et Informatica Universitatis Ostraviensis
1 Functional Analysis and Other Mathematics
1 Journal of Physics A: Mathematical and Theoretical
1 Pacific Journal of Applied Mathematics

Publications by Year

Citations contained in zbMATH Open

142 Publications have been cited 868 times in 501 Documents Cited by Year
The Riemann zeta-function. Transl. from the Russian by Neal Koblitz. Zbl 0756.11022
Karatsuba, A. A.; Voronin, S. M.
107
1992
Basic analytic number theory. Transl. from the Russian by Melvyn B. Nathanson. Zbl 0767.11001
Karatsuba, A.
42
1993
Trigonometric sums in number theory and analysis. Transl. from the Russian. Zbl 1074.11043
Arkhipov, G. I.; Chubarikov, V. N.; Karatsuba, A. A.
41
2004
The Riemann zeta-function. Zbl 0836.11029
Voronin, S. M.; Karatsuba, A. A.
33
1994
Theory of multiple trigonometric sums. Zbl 0638.10037
Arkhipov, G. I.; Karatsuba, A. A.; Chubarikov, V. N.
33
1987
Fractional parts of functions of a special form. Zbl 0874.11050
Karatsuba, A. A.
22
1995
The argument of the Riemann zeta function. Zbl 1116.11070
Karatsuba, A. A.; Korolev, M. A.
17
2005
On the zeros of the Riemann zeta-function on short intervals of the critical line. Zbl 0545.10025
Karatsuba, A. A.
17
1983
Some problems of contemporary analytic number theory. Zbl 0315.10039
Karatsuba, A. A.
15
1975
The distribution of values of Dirichlet characters on additive sequences. Zbl 0772.11028
Karatsuba, A. A.
14
1991
Behaviour of the argument of the Riemann zeta function on the critical line. Zbl 1215.11081
Karatsuba, A. A.; Korolev, M. A.
13
2006
Analogues of Kloostermans sums. Zbl 0897.11028
Karatsuba, A. A.
13
1995
Estimates of complete trigonometric sums. Zbl 0154.29804
Karatsuba, A. A.
13
1967
Kloosterman double sums. Zbl 0971.11045
Karatsuba, A. A.
12
1999
Analogues of incomplete Kloosterman sums and their applications. Zbl 0978.11037
Karatsuba, Anatoliĭ A.
12
1997
Complex analysis in number theory. Zbl 0856.11038
Karatsuba, A. A.
12
1995
Trigonometric integrals. Zbl 0493.10040
Arkhipov, G. I.; Karatsuba, A. A.; Chubarikov, V. N.
12
1980
An estimate of the \(L_1\)-norm of an exponential sum. Zbl 0924.11065
Karatsuba, A. A.
11
1998
The Riemann zeta-function and its zeros. Zbl 0594.10026
Karatsuba, A. A.
11
1985
On character sums and the exceptional set of a congruence problem. Zbl 1135.11044
Garaev, M. Z.; Karatsuba, A. A.
10
2005
Sums of fractional parts of functions of a special form. Zbl 0918.11038
Karatsuba, A. A.
10
1996
Approximation of exponential sums by shorter ones. Zbl 0648.10023
Karatsuba, A. A.
10
1987
The representation of residue classes by products of small integers. Zbl 1197.11003
Garaev, M. Z.; Karatsuba, A. A.
9
2007
A refinement of theorems on the number of zeros lying on intervals of the critical line of certain Dirichlet series. Zbl 0798.11033
Karatsuba, A. A.
9
1992
On the distance between adjacent zeros of the Riemann zeta-function lying on the critical line. Zbl 0472.10040
Karatsuba, A. A.
9
1981
Weighted character sums. Zbl 0963.11046
Karatsuba, A. A.
8
2000
The complexity of computations. Zbl 0872.68068
Karatsuba, A. A.
8
1995
On the zeros of the Davenport-Heilbronn function on the critical line. Zbl 0701.11028
Karatsuba, A. A.
8
1990
A theorem on the approximation of a trigonometric sum by a shorter one. Zbl 1168.11030
Karatsuba, A. A.; Korolev, M. A.
7
2007
The distribution of inverses in a residue ring modulo a given modulus. Zbl 0826.11032
Karatsuba, A. A.
7
1993
On the function G(n) in Waring’s problem. Zbl 0594.10041
Karatsuba, A. A.
7
1985
Multiple trigonometric sums. Zbl 0441.10037
Arkhipov, G. I.; Karatsuba, A. A.; Chubarikov, V. N.
7
1980
Principles of analytic number theory. (Osnovy analiticheskoj teorii chisel). Zbl 0428.10019
Karatsuba, A. A.
7
1975
Character sums and primitive roots in finite fields. Zbl 0182.37501
Karatsuba, A. A.
7
1968
A resummation formula for collapse and revival in the Jaynes-Cummings model. Zbl 1163.81016
Karatsuba, Anatolii A.; Karatsuba, Ekatherina A.
6
2009
Arithmetic problems in the theory of Dirichlet characters. Zbl 1230.11099
Karatsuba, A. A.
6
2008
Zero multiplicity and lower bound estimates of \(|\zeta(S)|\). Zbl 1196.11118
Karatsuba, Anatolii A.
6
2006
Lower bounds for the maximum modulus of \(\zeta(s)\) in small domains of the critical strip. Zbl 1137.11332
Karatsuba, A. A.
6
2001
The method of trigonometric sums in number theory. Zbl 0549.10027
Vinogradov, I. M.; Karatsuba, A. A.
6
1984
On the zeros of the function \(\zeta(s)\) on short intervals of the critical line. Zbl 0545.10026
Karatsuba, A. A.
6
1984
On a local representation of zero by a form. Zbl 0476.10018
Arkhipov, G. I.; Karatsuba, A. A.
6
1981
Sums of Legendre symbols of polynomials of second degree over prime numbers. Zbl 0403.10016
Karatsuba, A. A.
6
1978
Estimates for trigonometric sams by Vinogradov’s method and some applications. Zbl 0226.10037
Karatsuba, A. A.
6
1971
Trigonometric sums of a special type and their applications. Zbl 0152.03402
Karatsuba, A. A.
6
1964
Applications of ATS in a quantum-optical model. Zbl 1297.81193
Karatsuba, Anatolii A.; Karatsuba, Ekatherina A.
5
2009
On zeros of special form of functions connected with Dirichlet series. Zbl 0737.11021
Karatsuba, A. A.
5
1991
On the zeros of the Davenport-Heilbronn function lying on the critical line. Zbl 0717.11035
Karatsuba, A. A.
5
1991
On the zeros of a special type of function connected with Dirichlet series. Zbl 0788.11033
Karatsuba, A. A.
5
1991
Distribution of zeros of the function \(\zeta (+it)\). Zbl 0558.10033
Karatsuba, A. A.
5
1984
The index of convergence of the singular integral in Tarry’s problem. Zbl 0432.10021
Arkhipov, G. I.; Karatsuba, A. A.; Chubarikov, V. N.
5
1979
Uniform approximation of the remainder term in the Dirichlet divisor problem. Zbl 0253.10035
Karatsuba, A. A.
5
1973
Distribution of power residues and nonresidues in additive sequences. Zbl 0234.10022
Karatsuba, A. A.
5
1971
A property of the set of prime numbers. Zbl 1246.11158
Karatsuba, A. A.
4
2011
New estimates of double trigonometric sums with exponential functions. Zbl 1175.11045
Garaev, M. Z.; Karatsuba, A. A.
4
2006
On the function \(S(t)\). Zbl 0898.11032
Karatsuba, A. A.
4
1996
A new approach to the problem of the zeros of some Dirichlet series. Zbl 0904.11024
Karatsuba, A. A.
4
1994
On the number of zeros of the Riemann zeta-function lying on almost all short intervals of the critical line. Zbl 0761.11034
Karatsuba, A. A.
4
1992
On zeros of the Riemann zeta-function on the critical line. Zbl 0566.10030
Karatsuba, A. A.
4
1985
Multiple trigonometric sums and their applications. Zbl 0446.10030
Arkhipov, G. I.; Karatsuba, A. A.; Chubarikov, V. N.
4
1980
An upper bound for the modulus of a multiple trigonometric sum. Zbl 0432.10020
Arkhipov, G. I.; Karatsuba, A. A.; Chubarikov, V. N.
4
1977
A system of congruences. Zbl 0333.10001
Karatsuba, A. A.
4
1976
Estimates for trigonometric sums by Vinogradov’s method, and some applications. Zbl 0259.10040
Karatsuba, A. A.
4
1973
The Dirichlet divisor problem in number fields. Zbl 0265.10011
Karatsuba, A. A.
4
1972
Eine gleichmäßige Abschätzung des Restgliedes im Dirichletschen Teilerproblem. Zbl 0239.10025
Karatsuba, A. A.
4
1972
On a certain arithmetic sum. Zbl 0227.10036
Karatsuba, A. A.
4
1971
On the mean-value theorem. Zbl 0142.29302
Karatsuba, A. A.; Korobov, N. M.
4
1963
Das Waringsche Problem für eine Kongruenz nach einem Modul, der gleich einer Primzahlpotenz ist. Zbl 0117.28206
Karatsuba, A. A.
4
1962
A property of the set of primes as a multiplicative basis of the natural numbers. Zbl 1252.11072
Karatsuba, A. A.
3
2011
Approximation of an exponential sum by a shorter one. Zbl 1327.11055
Karatsuba, A. A.; Korolev, M. A.
3
2007
On the number of sign changes of the function \(R_1(x)\) and its mean values. Zbl 1148.11049
Karatsuba, A. A.
3
2005
On the approximation of \(\pi(x)\). Zbl 1136.11057
Karatsuba, A. A.
3
2004
On lower bounds for the maximum modulus of the Riemann zeta function on short intervals of the critical line. Zbl 1167.11315
Karatsuba, A. A.
3
2004
Fractional moments and zeros of \(\zeta(s)\) on the critical line. Zbl 1137.11333
Karatsuba, A. A.
3
2002
On lower bounds for the Riemann zeta-function. Zbl 1047.11082
Karatsuba, A. A.
3
2001
Additive congruences. Zbl 0922.11077
Karatsuba, A. A.
3
1997
A multidimensional analogue of Waring’s problem. Zbl 0655.10043
Arkhipov, G. I.; Karatsuba, A. A.
3
1987
Riemann’s zeta-function and its zeros. Zbl 0589.10040
Karatsuba, A. A.
3
1985
On the zeros of the function \(\zeta(s)\) on short intervals of the critical line. Zbl 0566.10031
Karatsuba, A. A.
3
1985
Multiple trigonometric sums. Zbl 0489.10030
Arkhipov, G. I.; Karatsuba, A. A.; Chubarikov, V. N.
3
1982
On the distribution of values of nonprincipal characters. Zbl 0413.10034
Karatsuba, A. A.
3
1976
Sums of characters in sequences of shifted prime numbers, with applications. Zbl 0315.10034
Karatsuba, A. A.
3
1975
Sums of characters with prime numbers in an arithmetic progression. Zbl 0224.10038
Karatsuba, A. A.
3
1971
The distribution of products of shifted primes in arithmetical progressions. Zbl 0224.10043
Karatsuba, A. A.
3
1970
Asymptotic formulas for a class of trigonometric sums. Zbl 0199.08802
Karatsuba, A. A.
3
1966
On application of the functional equation of the Jacobi Theta function to approximation of atomic inversion in the Jaynes-Cummings model. Zbl 1356.81248
Karatsuba, Anatolii A.; Karatsuba, Ekatherina A.
2
2010
Omega theorems for zeta sums. Zbl 1035.11035
Karatsuba, A. A.
2
2003
On fractional parts of rapidly growing functions. Zbl 1028.11045
Karatsuba, A. A.
2
2001
Sums of characters with prime numbers and their applications. Zbl 0992.11051
Karatsuba, Anatolij A.
2
2000
The multidimensional Dirichlet divisor problem and zero free regions for the Riemann zeta function. Zbl 0977.11042
Karatsuba, A. A.
2
2000
Arithmetical problems with numbers of special type. Zbl 0951.11028
Karatsuba, A. A.; Novak, B.
2
1999
On the zeros of arithmetic Dirichlet series without Euler product. Zbl 0820.11051
Karatsuba, A. A.
2
1993
On the zeros of a class of functions generated by the Hurwitz function. Zbl 0815.11043
Karatsuba, A. A.
2
1993
On zeros of the Davenport-Heilbronn function. Zbl 0796.11035
Karatsuba, A. A.
2
1992
Zeros of linear combinations of \(Z\)-functions corresponding to Dirichlet series. Zbl 0752.11034
Karatsuba, A. A.
2
1991
Zeros of certain Dirichlet series. Zbl 0701.11029
Karatsuba, A. A.
2
1990
Distribution of pairs of quadratic residues and nonresidues of special form. Zbl 0637.10025
Karatsuba, A. A.
2
1987
The distribution of zeros of the function \(\zeta (1/2+it)\). Zbl 0584.10019
Karatsuba, A. A.
2
1985
On the real zeros of the function \(\zeta (1/2+it)\). Zbl 0584.10018
Karatsuba, A. A.
2
1985
Peculiar cases of the theory of multiple trigonometric sums. Zbl 0536.10031
Arkhipov, G. I.; Karatsuba, A. A.; Chubarikov, V. N.
2
1983
On the distance between adjacent zeros of the Riemann zeta function lying on the critical line. Zbl 0518.10045
Karatsuba, A. A.
2
1983
Comments to my works, written by myself. Zbl 1302.01045
Karatsuba, A. A.
1
2013
A property of the set of prime numbers. Zbl 1246.11158
Karatsuba, A. A.
4
2011
A property of the set of primes as a multiplicative basis of the natural numbers. Zbl 1252.11072
Karatsuba, A. A.
3
2011
Euler and number theory. Zbl 1316.11002
Karatsuba, A. A.
1
2011
Physical mathematics in number theory. Zbl 1253.11081
Karatsuba, Anatolii A.; Karatsuba, Ekatherina A.
1
2011
On application of the functional equation of the Jacobi Theta function to approximation of atomic inversion in the Jaynes-Cummings model. Zbl 1356.81248
Karatsuba, Anatolii A.; Karatsuba, Ekatherina A.
2
2010
New estimates of short Kloosterman sums. Zbl 1271.11083
Karatsuba, A. A.
1
2010
A resummation formula for collapse and revival in the Jaynes-Cummings model. Zbl 1163.81016
Karatsuba, Anatolii A.; Karatsuba, Ekatherina A.
6
2009
Applications of ATS in a quantum-optical model. Zbl 1297.81193
Karatsuba, Anatolii A.; Karatsuba, Ekatherina A.
5
2009
Euler and number theory. Zbl 1312.01015
Karatsuba, A. A.
1
2009
Arithmetic problems in the theory of Dirichlet characters. Zbl 1230.11099
Karatsuba, A. A.
6
2008
Nonlinear sums of characters over primes. Zbl 1221.11175
Karatsuba, A. A.
1
2008
The representation of residue classes by products of small integers. Zbl 1197.11003
Garaev, M. Z.; Karatsuba, A. A.
9
2007
A theorem on the approximation of a trigonometric sum by a shorter one. Zbl 1168.11030
Karatsuba, A. A.; Korolev, M. A.
7
2007
Approximation of an exponential sum by a shorter one. Zbl 1327.11055
Karatsuba, A. A.; Korolev, M. A.
3
2007
Behaviour of the argument of the Riemann zeta function on the critical line. Zbl 1215.11081
Karatsuba, A. A.; Korolev, M. A.
13
2006
Zero multiplicity and lower bound estimates of \(|\zeta(S)|\). Zbl 1196.11118
Karatsuba, Anatolii A.
6
2006
New estimates of double trigonometric sums with exponential functions. Zbl 1175.11045
Garaev, M. Z.; Karatsuba, A. A.
4
2006
Korobov trigonometric sums. Zbl 1241.11096
Karatsuba, A. A.
1
2006
The argument of the Riemann zeta function. Zbl 1116.11070
Karatsuba, A. A.; Korolev, M. A.
17
2005
On character sums and the exceptional set of a congruence problem. Zbl 1135.11044
Garaev, M. Z.; Karatsuba, A. A.
10
2005
On the number of sign changes of the function \(R_1(x)\) and its mean values. Zbl 1148.11049
Karatsuba, A. A.
3
2005
Trigonometric sums in number theory and analysis. Transl. from the Russian. Zbl 1074.11043
Arkhipov, G. I.; Chubarikov, V. N.; Karatsuba, A. A.
41
2004
On the approximation of \(\pi(x)\). Zbl 1136.11057
Karatsuba, A. A.
3
2004
On lower bounds for the maximum modulus of the Riemann zeta function on short intervals of the critical line. Zbl 1167.11315
Karatsuba, A. A.
3
2004
On the Riemann asymptotic formula for \(\pi(x)\). Zbl 1234.11123
Karatsuba, A. A.
1
2004
Omega theorems for zeta sums. Zbl 1035.11035
Karatsuba, A. A.
2
2003
Zeros and local extrema of trigonometric sums. Zbl 1081.11058
Karatsuba, A. A.
1
2003
Fractional moments and zeros of \(\zeta(s)\) on the critical line. Zbl 1137.11333
Karatsuba, A. A.
3
2002
On zeros of trigonometric sums. Zbl 1223.11099
Karatsuba, A. A.
1
2002
Lower bounds for the maximum modulus of \(\zeta(s)\) in small domains of the critical strip. Zbl 1137.11332
Karatsuba, A. A.
6
2001
On lower bounds for the Riemann zeta-function. Zbl 1047.11082
Karatsuba, A. A.
3
2001
On fractional parts of rapidly growing functions. Zbl 1028.11045
Karatsuba, A. A.
2
2001
Weighted character sums. Zbl 0963.11046
Karatsuba, A. A.
8
2000
Sums of characters with prime numbers and their applications. Zbl 0992.11051
Karatsuba, Anatolij A.
2
2000
The multidimensional Dirichlet divisor problem and zero free regions for the Riemann zeta function. Zbl 0977.11042
Karatsuba, A. A.
2
2000
Kloosterman double sums. Zbl 0971.11045
Karatsuba, A. A.
12
1999
Arithmetical problems with numbers of special type. Zbl 0951.11028
Karatsuba, A. A.; Novak, B.
2
1999
An estimate of the \(L_1\)-norm of an exponential sum. Zbl 0924.11065
Karatsuba, A. A.
11
1998
Regular sets in residue classes. Zbl 0922.11078
Karatsuba, A. A.
1
1998
Analogues of incomplete Kloosterman sums and their applications. Zbl 0978.11037
Karatsuba, Anatoliĭ A.
12
1997
Additive congruences. Zbl 0922.11077
Karatsuba, A. A.
3
1997
Sums of fractional parts of functions of a special form. Zbl 0918.11038
Karatsuba, A. A.
10
1996
On the function \(S(t)\). Zbl 0898.11032
Karatsuba, A. A.
4
1996
Density theorem and the behavior of the argument of the Riemann zeta function. Zbl 1059.11510
Karatsuba, A. A.
1
1996
Fractional parts of functions of a special form. Zbl 0874.11050
Karatsuba, A. A.
22
1995
Analogues of Kloostermans sums. Zbl 0897.11028
Karatsuba, A. A.
13
1995
Complex analysis in number theory. Zbl 0856.11038
Karatsuba, A. A.
12
1995
The complexity of computations. Zbl 0872.68068
Karatsuba, A. A.
8
1995
The Riemann zeta-function. Zbl 0836.11029
Voronin, S. M.; Karatsuba, A. A.
33
1994
A new approach to the problem of the zeros of some Dirichlet series. Zbl 0904.11024
Karatsuba, A. A.
4
1994
Zeros of the arithmetical Dirichlet series. Zbl 0824.11053
Karatsuba, Anatolij Alekseevich
1
1994
Basic analytic number theory. Transl. from the Russian by Melvyn B. Nathanson. Zbl 0767.11001
Karatsuba, A.
42
1993
The distribution of inverses in a residue ring modulo a given modulus. Zbl 0826.11032
Karatsuba, A. A.
7
1993
On the zeros of arithmetic Dirichlet series without Euler product. Zbl 0820.11051
Karatsuba, A. A.
2
1993
On the zeros of a class of functions generated by the Hurwitz function. Zbl 0815.11043
Karatsuba, A. A.
2
1993
The Riemann zeta-function. Transl. from the Russian by Neal Koblitz. Zbl 0756.11022
Karatsuba, A. A.; Voronin, S. M.
107
1992
A refinement of theorems on the number of zeros lying on intervals of the critical line of certain Dirichlet series. Zbl 0798.11033
Karatsuba, A. A.
9
1992
On the number of zeros of the Riemann zeta-function lying on almost all short intervals of the critical line. Zbl 0761.11034
Karatsuba, A. A.
4
1992
On zeros of the Davenport-Heilbronn function. Zbl 0796.11035
Karatsuba, A. A.
2
1992
The distribution of values of Dirichlet characters on additive sequences. Zbl 0772.11028
Karatsuba, A. A.
14
1991
On zeros of special form of functions connected with Dirichlet series. Zbl 0737.11021
Karatsuba, A. A.
5
1991
On the zeros of the Davenport-Heilbronn function lying on the critical line. Zbl 0717.11035
Karatsuba, A. A.
5
1991
On the zeros of a special type of function connected with Dirichlet series. Zbl 0788.11033
Karatsuba, A. A.
5
1991
Zeros of linear combinations of \(Z\)-functions corresponding to Dirichlet series. Zbl 0752.11034
Karatsuba, A. A.
2
1991
On the zeros of the Davenport-Heilbronn function on the critical line. Zbl 0701.11028
Karatsuba, A. A.
8
1990
Zeros of certain Dirichlet series. Zbl 0701.11029
Karatsuba, A. A.
2
1990
The distribution of prime numbers. Zbl 0715.11046
Karatsuba, A. A.
1
1990
Theory of multiple trigonometric sums. Zbl 0638.10037
Arkhipov, G. I.; Karatsuba, A. A.; Chubarikov, V. N.
33
1987
Approximation of exponential sums by shorter ones. Zbl 0648.10023
Karatsuba, A. A.
10
1987
A multidimensional analogue of Waring’s problem. Zbl 0655.10043
Arkhipov, G. I.; Karatsuba, A. A.
3
1987
Distribution of pairs of quadratic residues and nonresidues of special form. Zbl 0637.10025
Karatsuba, A. A.
2
1987
The Hilbert-Kamke problem in analytic number theory. Zbl 0619.10014
Karatsuba, A. A.
1
1987
The method of trigonometric sums in number theory. Zbl 0603.10037
Vinogradov, I. M.; Karatsuba, A. A.
1
1986
On the zeros of the function \(\zeta(s)\) in the neighborhood of the critical line. Zbl 0582.10027
Karatsuba, A. A.
1
1986
The Riemann zeta-function and its zeros. Zbl 0594.10026
Karatsuba, A. A.
11
1985
On the function G(n) in Waring’s problem. Zbl 0594.10041
Karatsuba, A. A.
7
1985
On zeros of the Riemann zeta-function on the critical line. Zbl 0566.10030
Karatsuba, A. A.
4
1985
Riemann’s zeta-function and its zeros. Zbl 0589.10040
Karatsuba, A. A.
3
1985
On the zeros of the function \(\zeta(s)\) on short intervals of the critical line. Zbl 0566.10031
Karatsuba, A. A.
3
1985
The distribution of zeros of the function \(\zeta (1/2+it)\). Zbl 0584.10019
Karatsuba, A. A.
2
1985
On the real zeros of the function \(\zeta (1/2+it)\). Zbl 0584.10018
Karatsuba, A. A.
2
1985
The method of trigonometric sums in number theory. Zbl 0549.10027
Vinogradov, I. M.; Karatsuba, A. A.
6
1984
On the zeros of the function \(\zeta(s)\) on short intervals of the critical line. Zbl 0545.10026
Karatsuba, A. A.
6
1984
Distribution of zeros of the function \(\zeta (+it)\). Zbl 0558.10033
Karatsuba, A. A.
5
1984
On the zeros of the Riemann zeta-function on short intervals of the critical line. Zbl 0545.10025
Karatsuba, A. A.
17
1983
Peculiar cases of the theory of multiple trigonometric sums. Zbl 0536.10031
Arkhipov, G. I.; Karatsuba, A. A.; Chubarikov, V. N.
2
1983
On the distance between adjacent zeros of the Riemann zeta function lying on the critical line. Zbl 0518.10045
Karatsuba, A. A.
2
1983
Multiple trigonometric sums. Zbl 0489.10030
Arkhipov, G. I.; Karatsuba, A. A.; Chubarikov, V. N.
3
1982
On a problem in the theory of congruences. Zbl 0508.10012
Arkhipov, G. I.; Karatsuba, A. A.
2
1982
On local representation of zero by a form. Zbl 0496.10010
Arkhipov, G. I.; Karatsuba, A. A.
2
1982
On the representation of zero by a form in the field of p-adic numbers. Zbl 0496.10009
Arkhipov, G. I.; Karatsuba, A. A.
2
1982
On the distance between adjacent zeros of the Riemann zeta-function lying on the critical line. Zbl 0472.10040
Karatsuba, A. A.
9
1981
On a local representation of zero by a form. Zbl 0476.10018
Arkhipov, G. I.; Karatsuba, A. A.
6
1981
On a problem with prime numbers. Zbl 0483.10043
Karatsuba, A. A.
1
1981
Ivan Matveevich Vinogradov (to his ninetieth birthday). Zbl 0475.01021
Karatsuba, A. A.
1
1981
Trigonometric integrals. Zbl 0493.10040
Arkhipov, G. I.; Karatsuba, A. A.; Chubarikov, V. N.
12
1980
Multiple trigonometric sums. Zbl 0441.10037
Arkhipov, G. I.; Karatsuba, A. A.; Chubarikov, V. N.
7
1980
Multiple trigonometric sums and their applications. Zbl 0446.10030
Arkhipov, G. I.; Karatsuba, A. A.; Chubarikov, V. N.
4
1980
On a system of Diophantine equations. Zbl 0478.10020
Arkhipov, G. I.; Karatsuba, A. A.; Chubarikov, V. N.
1
1980
...and 42 more Documents
all top 5

Cited by 403 Authors

30 Korolëv, Maksim Aleksandrovich
25 Chubarikov, Vladimir Nikolaevich
25 Laurinčikas, Antanas
25 Shparlinski, Igor E.
19 Karatsuba, Anatoliĭ Alekseevich
16 Garaev, Moubariz Z.
13 Gritsenko, Svetlana Aleksandrovna
10 Coffey, Mark William
9 Mishou, Hidehiko
9 Rakhmonov, Zarullo Khusenovich
6 Boyarinov, R. N.
6 Ivić, Aleksandar P.
6 Karatsuba, Ekaterina Anatol’evna
6 Shkredov, Il’ya Dmitrievich
6 Tolev, Doychin I.
6 Wooley, Trevor D.
5 Garunkštis, Ramūnas
5 Katz, Daniel J.
5 Konyagin, Sergeĭ Vladimirovich
5 Pankowski, Łukasz
4 Arkhipov, Gennadiĭ Ivanovich
4 Bourgain, Jean
4 Changa, Maris E.
4 Deza, Elena Ivanovna
4 Èminyan, Karapet Mkrtichevich
4 Ikromov, Isroil A.
4 Jutila, Matti Ilmari
4 Macaitienė, Renata
4 Nagoshi, Hirofumi
4 Šiaučiūnas, Darius
4 Steuding, Jörn
3 Alzer, Horst
3 Banks, William D.
3 Carneiro, Emanuel
3 Chang, Mei-Chu
3 Do Duc Tam
3 Dzhabbarov, Ilgar Shikar
3 García, Victor Cuauhtemoc
3 Gauthier, Paul M.
3 Götze, Friedrich W.
3 Langevin, Philippe
3 Lee, Yoonbok
3 Maslov, Viktor Pavlovich
3 Matsumoto, Kohji
3 Mit’kin, Dmitriĭ Alekseevich
3 Nakamura, Takashi
3 Naumenko, Anton Pavlovich
3 Popov, Dmitrii A.
3 Rakhmonov, Firuz Zarulloevich
3 Rakhmonov, P. Z.
3 Rezvyakova, Irina S.
3 Saliba, Holem Mansour
3 Shubin, Andrei V.
3 Tanigawa, Yoshio
3 Varukhina, Lidiya Vladimirovna
2 Albeverio, Sergio A.
2 Alkan, Emre
2 Blackburn, Simon R.
2 Bredikhin, Boris Maksimovich
2 Brüdern, Jörg
2 Chan, Tsz Ho
2 Cochrane, Todd
2 Demidov, D. B.
2 Dubickas, Artūras
2 Fujii, Akio
2 Ham, Seheon
2 Hu, Liqun
2 Kalmynin, A. B.
2 Kerr, Bryce
2 Kolesnik, Grigoriĭ Abramovich
2 Kolodyazhny, V. M.
2 Kolpakova, Ol’ga Viktorovna
2 Kumchev, Angel V.
2 Kunik, Matthias
2 Lapidus, Michel L.
2 Malykhin, Yuriĭ Vyacheslavovich
2 Meng, Xianchang
2 Misevičius, G. A.
2 Mot’kina, N. N.
2 Motohashi, Yoichi
2 Muranov, Shakhriddin Abdullaevich
2 Odžak, Almasa
2 Robert, Olivier
2 Sharapova, M. L.
2 Shen, Chun-Yen
2 Timofeev, Nikolaĭ Mikhaĭlovich
2 Trudgian, Timothy S.
2 Trushechkin, Anton Sergeevich
2 Ul’yanov, Vladimir Vasil’evich
2 Volostnov, A. S.
2 Volovich, Igor’ Vasil’evich
2 Winterhof, Arne
2 Yao, Weili
2 Yao, Yanjun
2 Yashiro, Yoshikatsu
2 Zhao, Xiaomei
1 Aaber, John W.
1 Andersson, Johan
1 Andrade, Julio Cesar
1 Arkhipova, Lyudmila Gennad’evna
...and 303 more Authors
all top 5

Cited in 133 Serials

83 Mathematical Notes
42 Journal of Number Theory
37 Proceedings of the Steklov Institute of Mathematics
36 Chebyshevskiĭ Sbornik
15 Moscow University Mathematics Bulletin
14 Lithuanian Mathematical Journal
13 Doklady Mathematics
7 Mathematische Zeitschrift
7 Journal of Mathematical Sciences (New York)
7 The Ramanujan Journal
6 Rocky Mountain Journal of Mathematics
6 Functiones et Approximatio. Commentarii Mathematici
6 Journal of Computational and Applied Mathematics
6 Proceedings of the American Mathematical Society
5 Archiv der Mathematik
5 Duke Mathematical Journal
5 Functional Analysis and its Applications
5 Journal of Approximation Theory
5 Monatshefte für Mathematik
5 Transactions of the American Mathematical Society
5 Journal de Théorie des Nombres de Bordeaux
5 International Journal of Number Theory
4 Journal of Mathematical Analysis and Applications
4 Mathematics of Computation
4 Mathematika
4 Indagationes Mathematicae. New Series
4 Finite Fields and their Applications
4 Sbornik: Mathematics
3 Acta Arithmetica
3 Advances in Mathematics
3 Proceedings of the Japan Academy. Series A
3 Forum Mathematicum
3 Linear Algebra and its Applications
3 Cybernetics and Systems Analysis
3 Izvestiya: Mathematics
2 Bulletin of the Australian Mathematical Society
2 Discrete Mathematics
2 Journal d’Analyse Mathématique
2 Journal of Mathematical Physics
2 Mathematical Proceedings of the Cambridge Philosophical Society
2 The Mathematical Intelligencer
2 Theory of Probability and its Applications
2 Glasgow Mathematical Journal
2 Journal of Combinatorial Theory. Series A
2 Journal of the Mathematical Society of Japan
2 Journal of Soviet Mathematics
2 Mathematische Annalen
2 Mathematische Nachrichten
2 Michigan Mathematical Journal
2 Siberian Mathematical Journal
2 Acta Mathematica Hungarica
2 Journal of Complexity
2 Geometric and Functional Analysis. GAFA
2 Integral Transforms and Special Functions
2 The Journal of Fourier Analysis and Applications
2 Acta Mathematica Sinica. English Series
2 Integers
2 Nonlinear Analysis. Modelling and Control
2 Comptes Rendus. Mathématique. Académie des Sciences, Paris
2 Computational Methods and Function Theory
2 International Journal of Geometric Methods in Modern Physics
1 Computers & Mathematics with Applications
1 Discrete Applied Mathematics
1 Indian Journal of Pure & Applied Mathematics
1 Israel Journal of Mathematics
1 Journal of Statistical Physics
1 Russian Mathematical Surveys
1 Theoretical and Mathematical Physics
1 Ukrainian Mathematical Journal
1 Chaos, Solitons and Fractals
1 Acta Mathematica
1 Annales de l’Institut Fourier
1 The Annals of Probability
1 Commentarii Mathematici Helvetici
1 The Journal of the Indian Mathematical Society. New Series
1 Journal für die Reine und Angewandte Mathematik
1 Manuscripta Mathematica
1 Mathematica Slovaca
1 Proceedings of the London Mathematical Society. Third Series
1 Publications of the Research Institute for Mathematical Sciences, Kyoto University
1 Quaestiones Mathematicae
1 Theoretical Computer Science
1 Tokyo Journal of Mathematics
1 Advances in Applied Mathematics
1 Zeitschrift für Analysis und ihre Anwendungen
1 Physica D
1 Journal of Symbolic Computation
1 Probability Theory and Related Fields
1 Constructive Approximation
1 SIAM Journal on Discrete Mathematics
1 Publicacions Matemàtiques
1 Séminaire de Théorie des Nombres de Bordeaux. Deuxième Série
1 The Journal of Geometric Analysis
1 Discrete Mathematics and Applications
1 Numerical Algorithms
1 Godishnik na Sofiĭskiya Universitet “Sv. Kliment Okhridski”. Fakultet po Matematika i Informatika
1 Computational Mathematics and Mathematical Physics
1 European Journal of Operational Research
1 Historia Mathematica
1 Bulletin of the American Mathematical Society. New Series
...and 33 more Serials
all top 5

Cited in 43 Fields

443 Number theory (11-XX)
35 Harmonic analysis on Euclidean spaces (42-XX)
20 Functions of a complex variable (30-XX)
17 Probability theory and stochastic processes (60-XX)
14 Quantum theory (81-XX)
13 Combinatorics (05-XX)
11 Approximations and expansions (41-XX)
11 Numerical analysis (65-XX)
10 Special functions (33-XX)
8 History and biography (01-XX)
8 Computer science (68-XX)
6 Partial differential equations (35-XX)
6 Information and communication theory, circuits (94-XX)
4 Algebraic geometry (14-XX)
4 Real functions (26-XX)
4 Dynamical systems and ergodic theory (37-XX)
4 Sequences, series, summability (40-XX)
4 Operator theory (47-XX)
4 Global analysis, analysis on manifolds (58-XX)
4 Statistical mechanics, structure of matter (82-XX)
3 Group theory and generalizations (20-XX)
3 Integral transforms, operational calculus (44-XX)
3 Statistics (62-XX)
2 Commutative algebra (13-XX)
2 Linear and multilinear algebra; matrix theory (15-XX)
2 Measure and integration (28-XX)
2 Manifolds and cell complexes (57-XX)
2 Operations research, mathematical programming (90-XX)
1 Field theory and polynomials (12-XX)
1 Potential theory (31-XX)
1 Several complex variables and analytic spaces (32-XX)
1 Ordinary differential equations (34-XX)
1 Difference and functional equations (39-XX)
1 Functional analysis (46-XX)
1 Geometry (51-XX)
1 Convex and discrete geometry (52-XX)
1 Differential geometry (53-XX)
1 General topology (54-XX)
1 Mechanics of deformable solids (74-XX)
1 Fluid mechanics (76-XX)
1 Relativity and gravitational theory (83-XX)
1 Biology and other natural sciences (92-XX)
1 Mathematics education (97-XX)

Citations by Year

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