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A. A. Karatsuba

– head of Department of Number Theory, Steklov Institute of Mathematics of Russian Academy of Sciences,

– professor of Department "Mathematical Analysis",
Faculty of Mechanics and Mathematics, M. V. Lomonosov Moscow State University (MSU)

Address: Department of Number Theory, Steklov Institute of Mathematics RAS
8, Gubkina str., 119991, Moscow, Russia

Tel.: (495) 938 37 32
Fax: (495) 135 05 55
Email: karatsuba@mi.ras.ru

Born 31.01.1937, Grozny

 Scientific interests
 Education and Professional Activities
 Prizes and Awards
 List of Research Works
 The paper: G. I. Archipov, V. N. Chubarikov "On the mathematical works of professor A. A. Karatsuba"
(Proc. Steklov Inst. Math., vol. 218, 1997).

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Scientific interests and works are in the field of analytic number theory and mathematical cybernetics:
1. Theory of trigonometric sums and trigonometric integrals:
  • the Tarry problem
  • the p-adic method
  • multiple trigonometric sums
  • estimating the Hardy function in the Waring problem
  • the Artin problem on local representation of zero by a form
  • the Hua Loo Keng problem on the index of convergence of the singular integral in the Tarry problem
  • estimating the short Kloostermans sums
  • a multidimensional analogue of Waring's problem
2. Theory of the Riemann zeta function:
  • the Selberg problem
  • zeros of linear combinations of L-series of Dirichlet
  • distribution of zeros of the Riemann zeta function on the short intervals of the critical line
  • the bound of zeros of the Riemann zeta function and the multidimensional Dirichlet divisor problem
  • lower bounds for the maximum modulus of zeta function in small domains of the critical strip and in short intervals of the critical line
  • the behavior of the argument of zeta function on the critical line
3. Theory of the Dirichlet characters:
  • estimating sums of characters in finite fields
  • estimating linear sums of characters in shifted prime numbers
  • estimating sums of characters of polynomials with prime argument
  • lower bounds for the sums of characters of polynomials
  • sums of characters on additive sequences
  • distribution of power residues and primitive roots in sparse sequences
4. Theory of finite automata:
  • the problem of sharp estimate of the least length of the experiment determining the state of the automaton in the end of the experiment
5. Theory of fast computations:
  • the first general method and algorithm for fast multiplication of multiplace numbers – the "divide and conquer" method which had served as the source of a new direction of investigations connected with fast computations
  • the complexity of the computation of the functions.
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Education and Professional Activities

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Prizes and Awards

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