Anatoly Karatsuba | Academic Influence

Anatoly Karatsuba's AcademicInfluence.com Rankings

Anatoly Karatsuba

Mathematics

#1873

World Rank

#2979

Historical Rank

Measure Theory

#4654

World Rank

#5450

Historical Rank

mathematics Degrees

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Mathematics

Why Is Anatoly Karatsuba Influential?

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According to Wikipedia, Anatoly Alexeyevich Karatsuba was a Russian mathematician working in the field of analytic number theory, p-adic numbers and Dirichlet series. For most of his student and professional life he was associated with the Faculty of Mechanics and Mathematics of Moscow State University, defending a D.Sc. there entitled "The method of trigonometric sums and intermediate value theorems" in 1966. He later held a position at the Steklov Institute of Mathematics of the Academy of Sciences.

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Anatoly Karatsuba's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Chapter I. The definition and the simplest properties of the Riemann zeta-function (1992) (34)
ON THE ZEROS OF THE DAVENPORT-HEILBRONN FUNCTION LYING ON THE CRITICAL LINE (1991) (32)
Arithmetic problems in the theory of Dirichlet characters (2008) (30)
On estimates of complete trigonometric sums (1967) (30)
Approximation of exponential sums by shorter ones (1987) (27)
On the function S(t) (1996) (24)
An estimate of theL1-norm of an exponential sum (1996) (24)
Kloosterman double sums (1999) (23)
New estimates of double trigonometric sums with exponential functions (2005) (22)
THE REPRESENTATION OF RESIDUE CLASSES BY PRODUCTS OF SMALL INTEGERS (2007) (21)
On character sums and the exceptional set of a congruence problem (2005) (21)
ON THE FUNCTION G(n) IN WARING'S PROBLEM (1986) (19)
ON THE ZEROS OF A SPECIAL TYPE OF FUNCTION CONNECTED WITH DIRICHLET SERIES (1992) (18)
THE DISTRIBUTION OF ZEROS OF THE FUNCTION ζ(1/2+it) (1985) (18)
The Riemann zeta function and its zeros (1985) (17)
SPECIAL CASES OF THE THEORY OF MULTIPLE TRIGONOMETRIC SUMS (1984) (13)
Density theorem and the behavior of the argument of the Riemann zeta function (1996) (12)
ON THE NUMBER OF ZEROS OF THE RIEMANN ZETA-FUNCTION LYING IN ALMOST ALL SHORT INTERVALS OF THE CRITICAL LINE (1993) (9)
Sums of characters in sequences of shifted prime numbers, with applications (1975) (8)
A property of the set of primes as a multiplicative basis of the natural numbers (2011) (8)
Lower bounds for the maximum modulus of the Riemann zeta function on short segments of the critical line (2004) (8)
Arithmetical problems with numbers of special type (1999) (7)
A refinement of theorems on the number of zeros lying on intervals of the critical line of certain Dirichlet series (1992) (7)
Fractional Moments and Zeros of ζ(s) on the Critical Line (2002) (6)
On zeros of certain Dirichlet series (1990) (6)
THE DISTRIBUTION OF PAIRS OF QUADRATIC RESIDUES AND NONRESIDUES OF A SPECIAL FORM (1988) (6)
Approximation of an exponential sum by a shorter one (2007) (6)
On a symmetric congruence and its applications (2005) (6)
New estimates of short Kloosterman sums (2010) (6)
On the Zeros of Arithmetic Dirichlet Series Without Euler Product (1994) (6)
ON THE ZEROS OF THE FUNCTION $ \zeta(s)$ ON SHORT INTERVALS OF THE CRITICAL LINE (1985) (6)
On the Riemann asymptotic formula for π(x) (2004) (5)
The multidimensional Dirichlet divisor problem and zero free regions for the Riemann zeta function (2000) (5)
Uniform estimates of multiple trigonometric sums (1980) (5)
On the Relationship between the Multidimensional Dirichlet Divisor Problem and the Boundary of Zeros of ζ(s)F (2001) (5)
The distribution of prime numbers (1990) (5)
Some problems of contemporary analytic number theorem (1975) (4)
Omega Theorems for Zeta Sums (2003) (4)
On the Zeros of Riemann’s Zeta-Function on the Critical Line (1991) (4)
Asymptotics of an arithmetic sum (1978) (4)
Comments to my works, written by myself (2013) (4)
On zeros of trigonometric sums (2002) (4)
Lower estimates of sums of polynomial characters (1973) (4)
On fractional parts of rapidly growing functions (2001) (3)
On a certain arithmetic function (1995) (3)
Lower Bounds for the Maximum Modulus of $$\zeta \left( s \right)$$ in Small Domains of the Critical Strip (2001) (3)
Behavior of the function R1(x) and its mean value (2005) (3)
Chapter 7. Special cases of the theory of multiple trigonometric sums (2004) (3)
On the real zeros of the function ζ(1/2 + it) (1985) (3)
Regular sets in residual classes (1998) (2)
Prof. RNDr. Břetislav Novák, DrSc. (1938–2003) would be seventy (2008) (2)
The method of trigonometric sums and theorems of the mean (1967) (2)
Nonlinear sums of characters over primes (2008) (2)
A system of congruences (1976) (2)
Chapter II. The Riemann zeta-function as a generating function in number theory (1992) (2)
COMMUNICATIONS OF THE MOSCOW MATHEMATICAL SOCIETY: On the zeros of a class of functions generated by the Hurwitz function (1993) (2)
Zeros and Local Extrema of Trigonometric Sums (2003) (2)
Euler and number theory (2011) (1)
About a system of indeterminate equations (1968) (1)
The Hilbert-Kamke problem in analytic number theory (1987) (1)
ON THE ZEROS OF THE FUNCTION ζ(s) IN THE NEIGHBORHOOD OF THE CRITICAL LINE (1986) (1)
Chapter 10. Estimates of multiple trigonometric sums with prime numbers (2004) (1)
A problem in the theory of congruences (1982) (1)
Euler and number theory (2009) (1)
Chapter 3. Weyl sums (2004) (0)
APPROXIMATION BY A "FLOATING" SYSTEM OF EXPONENTIALS ON CLASSES OF SMOOTH PERIODIC (2017) (0)
Chapter VI. Zeros of the zeta-function on the critical line (1992) (0)
Chapter 2. Rational trigonometric sums (2004) (0)
The distribution of values of non-principal characters in lacunary sequences (2016) (0)
Chapter 5. Estimates for multiple trigonometric sums (2004) (0)
Chapter VII. Distribution of nonzero values of the Riemann zeta-function (1992) (0)
Cosmology and zeta (2017) (0)
Chapter 1. Trigonometric integrals (2004) (0)
On zeros of certain Dirichlet series (2017) (0)
Chapter V. Density theorems (1992) (0)
On local representation of zero by a form (2017) (0)
Chapter 9. The p-adic method in three problems of number theory (2004) (0)
Incomplete Kloosterman sums and their applications (2016) (0)
Chapter III. Approximate functional equations (1992) (0)
Chapter 11. Some applications of trigonometric sums and integrals (2004) (0)
Chapter IV. Vinogradov’s method in the theory of the Riemann zeta-function (1992) (0)
Chapter 12. Short Kloosterman sums (2004) (0)
Chapter VIII. Ω-theorems (1992) (0)
Chapter 8. The Hilbert-Kamke problem and its generalizations (2004) (0)
Comments to my works, written by myself (2013) (0)
Chapter 4. Mean value theorems for multiple trigonometric sums (2004) (0)
Chapter 6. Several applications (2004) (0)

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What Schools Are Affiliated With Anatoly Karatsuba?

Anatoly Karatsuba is affiliated with the following schools:

Moscow State University

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