
– 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

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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 padic 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 Lseries 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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