Anatoly Karatsuba, the Glossary

Table of Contents

1. 57 relations: Analytic number theory, André Weil, Andrey Kolmogorov, Atle Selberg, ATS theorem, Brun–Titchmarsh theorem, Dirichlet character, Dirichlet L-function, Dirichlet series, Divide-and-conquer algorithm, Doctor of Sciences, Emil Artin, FEE method, Finite field, G. H. Hardy, Grozny, Guy Terjanian, Hendrik Kloosterman, Henryk Iwaniec, Hermann Weyl, Hua Luogeng, Ivan Vinogradov, Jaynes–Cummings model, John Friedlander, Karatsuba algorithm, Kloosterman sum, Leonard Carlitz, Mathematician, Moore machine, Moscow, Moscow State University, MSU Faculty of Mechanics and Mathematics, Multiplication, Nikolay Korobov, P-adic number, Parity problem (sieve theory), Prouhet–Tarry–Escott problem, Quantum field theory, Quantum optics, Quasi-algebraically closed field, Riemann hypothesis, Riemann zeta function, Roger Heath-Brown, Russia, Russian Academy of Sciences, Russians, Soviet Union, Special case, Steklov Institute of Mathematics, The Art of Computer Programming, ... Expand index (7 more) »

Analytic number theory

In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers.

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André Weil

André Weil (6 May 1906 – 6 August 1998) was a French mathematician, known for his foundational work in number theory and algebraic geometry.

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Andrey Kolmogorov

Andrey Nikolaevich Kolmogorov (a, 25 April 1903 – 20 October 1987) was a Soviet mathematician who contributed to the mathematics of probability theory, topology, intuitionistic logic, turbulence, classical mechanics, algorithmic information theory and computational complexity. Anatoly Karatsuba and Andrey Kolmogorov are 20th-century Russian mathematicians, Russian scientists and Soviet mathematicians.

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Atle Selberg

Atle Selberg (14 June 1917 – 6 August 2007) was a Norwegian mathematician known for his work in analytic number theory and the theory of automorphic forms, and in particular for bringing them into relation with spectral theory. Anatoly Karatsuba and Atle Selberg are number theorists.

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ATS theorem

In mathematics, the ATS theorem is the theorem on the approximation of a '''t'''rigonometric '''s'''um by a shorter one.

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Brun–Titchmarsh theorem

In analytic number theory, the Brun–Titchmarsh theorem, named after Viggo Brun and Edward Charles Titchmarsh, is an upper bound on the distribution of prime numbers in arithmetic progression.

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Dirichlet character

In analytic number theory and related branches of mathematics, a complex-valued arithmetic function \chi:\mathbb\rightarrow\mathbb is a Dirichlet character of modulus m (where m is a positive integer) if for all integers a and b.

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Dirichlet L-function

In mathematics, a Dirichlet L-series is a function of the form where \chi is a Dirichlet character and s a complex variable with real part greater than 1.

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Dirichlet series

In mathematics, a Dirichlet series is any series of the form \sum_^\infty \frac, where s is complex, and a_n is a complex sequence.

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Divide-and-conquer algorithm

In computer science, divide and conquer is an algorithm design paradigm.

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Doctor of Sciences

Doctor of Sciences (p, abbreviated д-р наук or д. н.; доктор наук; доктор на науките; доктар навук) is a higher doctoral degree in the Russian Empire, Soviet Union and many post-Soviet countries, which may be earned after the Candidate of Sciences.

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Emil Artin

Emil Artin (March 3, 1898 – December 20, 1962) was an Austrian mathematician of Armenian descent. Anatoly Karatsuba and Emil Artin are number theorists.

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FEE method

In mathematics, the FEE method, or fast E-function evaluation method, is the method of fast summation of series of a special form.

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Finite field

In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.

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G. H. Hardy

Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis. Anatoly Karatsuba and G. H. Hardy are mathematical analysts.

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Grozny

Grozny (Groznyy,; translit) is the capital city of Chechnya, Russia.

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Guy Terjanian

Guy Terjanian is a French mathematician who has worked on algebraic number theory.

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Hendrik Kloosterman

Hendrik Douwe Kloosterman (9 April 1900 – 6 May 1968) was a Dutch mathematician, known for his work in number theory (in particular, for introducing Kloosterman sums) and in representation theory. Anatoly Karatsuba and Hendrik Kloosterman are number theorists.

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Henryk Iwaniec

Henryk Iwaniec (born October 9, 1947) is a Polish-American mathematician, and since 1987 a professor at Rutgers University. Anatoly Karatsuba and Henryk Iwaniec are number theorists.

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Hermann Weyl

Hermann Klaus Hugo Weyl, (9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist, logician and philosopher.

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Hua Luogeng

Hua Luogeng or Hua Loo-Keng (12 November 1910 – 12 June 1985) was a Chinese mathematician and politician famous for his important contributions to number theory and for his role as the leader of mathematics research and education in the People's Republic of China. Anatoly Karatsuba and Hua Luogeng are number theorists.

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Ivan Vinogradov

Ivan Matveevich Vinogradov (a; 14 September 1891 – 20 March 1983) was a Soviet mathematician, who was one of the creators of modern analytic number theory, and also a dominant figure in mathematics in the USSR. Anatoly Karatsuba and Ivan Vinogradov are number theorists, Russian scientists and Soviet mathematicians.

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Jaynes–Cummings model

The Jaynes–Cummings model (sometimes abbreviated JCM) is a theoretical model in quantum optics.

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John Friedlander

John Friedlander is a Canadian mathematician specializing in analytic number theory. Anatoly Karatsuba and John Friedlander are number theorists.

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Karatsuba algorithm

The Karatsuba algorithm is a fast multiplication algorithm.

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Kloosterman sum

In mathematics, a Kloosterman sum is a particular kind of exponential sum.

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Leonard Carlitz

Leonard Carlitz (December 26, 1907 – September 17, 1999) was an American mathematician.

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Mathematician

A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.

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Moore machine

In the theory of computation, a Moore machine is a finite-state machine whose current output values are determined only by its current state.

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Moscow

Moscow is the capital and largest city of Russia.

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Moscow State University

Moscow State University (MSU; Moskovskiy gosudarstvennyy universitet) is a public research university in Moscow, Russia.

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MSU Faculty of Mechanics and Mathematics

The MSU Faculty of Mechanics and Mathematics (Механико-математический факультет МГУ) is a faculty of Moscow State University.

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Multiplication

Multiplication (often denoted by the cross symbol, by the mid-line dot operator, by juxtaposition, or, on computers, by an asterisk) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division.

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Nikolay Korobov

Nikolai Mikhailovich Korobov (Коробов Николай Михайлович; November 23, 1917 – October 25, 2004) was a Soviet mathematician specializing in number theory and numerical analysis. Anatoly Karatsuba and Nikolay Korobov are number theorists and Soviet mathematicians.

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P-adic number

In number theory, given a prime number, the -adic numbers form an extension of the rational numbers which is distinct from the real numbers, though with some similar properties; -adic numbers can be written in a form similar to (possibly infinite) decimals, but with digits based on a prime number rather than ten, and extending to the left rather than to the right.

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Parity problem (sieve theory)

In number theory, the parity problem refers to a limitation in sieve theory that prevents sieves from giving good estimates in many kinds of prime-counting problems.

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Prouhet–Tarry–Escott problem

In mathematics, the Prouhet–Tarry–Escott problem asks for two disjoint multisets A and B of n integers each, whose first k power sum symmetric polynomials are all equal.

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Quantum field theory

In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics.

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Quantum optics

Quantum optics is a branch of atomic, molecular, and optical physics dealing with how individual quanta of light, known as photons, interact with atoms and molecules.

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Quasi-algebraically closed field

In mathematics, a field F is called quasi-algebraically closed (or C1) if every non-constant homogeneous polynomial P over F has a non-trivial zero provided the number of its variables is more than its degree.

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Riemann hypothesis

In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part.

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Riemann zeta function

The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter (zeta), is a mathematical function of a complex variable defined as \zeta(s).

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Roger Heath-Brown

David Rodney "Roger" Heath-Brown (born 12 October 1952) is a British mathematician working in the field of analytic number theory.

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Russia

Russia, or the Russian Federation, is a country spanning Eastern Europe and North Asia.

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Russian Academy of Sciences

The Russian Academy of Sciences (RAS; Росси́йская акаде́мия нау́к (РАН) Rossíyskaya akadémiya naúk) consists of the national academy of Russia; a network of scientific research institutes from across the Russian Federation; and additional scientific and social units such as libraries, publishing units, and hospitals.

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Russians

Russians (russkiye) are an East Slavic ethnic group native to Eastern Europe.

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Soviet Union

The Union of Soviet Socialist Republics (USSR), commonly known as the Soviet Union, was a transcontinental country that spanned much of Eurasia from 1922 to 1991.

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Special case

In logic, especially as applied in mathematics, concept is a special case or specialization of concept precisely if every instance of is also an instance of but not vice versa, or equivalently, if is a generalization of.

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Steklov Institute of Mathematics

Steklov Institute of Mathematics or Steklov Mathematical Institute (Математический институт имени В.А.Стеклова) is a premier research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences.

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The Art of Computer Programming

The Art of Computer Programming (TAOCP) is a comprehensive monograph written by the computer scientist Donald Knuth presenting programming algorithms and their analysis.

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Theoretical physics

Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict natural phenomena.

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Toom–Cook multiplication

Toom–Cook, sometimes known as Toom-3, named after Andrei Toom, who introduced the new algorithm with its low complexity, and Stephen Cook, who cleaned the description of it, is a multiplication algorithm for large integers.

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Waring's problem

In number theory, Waring's problem asks whether each natural number k has an associated positive integer s such that every natural number is the sum of at most s natural numbers raised to the power k. For example, every natural number is the sum of at most 4 squares, 9 cubes, or 19 fourth powers.

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Yuri Linnik

Yuri Vladimirovich Linnik (Ю́рий Влади́мирович Ли́нник; January 8, 1915 – June 30, 1972) was a Soviet mathematician active in number theory, probability theory and mathematical statistics. Anatoly Karatsuba and Yuri Linnik are 20th-century Russian mathematicians, number theorists, Russian scientists and Soviet mathematicians.

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1981 in science

The year 1981 in science and technology involved many significant events, listed below.

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1999 in science

The year 1999 in science and technology involved some significant events.

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2001 in science

The year 2001 in science and technology involved many events, some of which are included below.

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References

[1] https://en.wikipedia.org/wiki/Anatoly_Karatsuba

Also known as A. A. Karacuba, A. A. Karatsuba, A.A. Karatsuba, Anatolii Alexeevitch Karatsuba, Anatolii Karatsuba, Karatsuba, Анато́лий Алексе́евич Карацу́ба.

, Theoretical physics, Toom–Cook multiplication, Waring's problem, Yuri Linnik, 1981 in science, 1999 in science, 2001 in science.